@article{Adin,
  title={The flag major index and group actions on polynomial rings},
  author={Adin, Ron M and Roichman, Yuval},
  journal={European Journal of Combinatorics},
  volume={22},
  number={4},
  pages={431--446},
  year={2001},
  publisher={Elsevier}
}

@article{arnold,
  title={The cohomology ring of the group of dyed braids},
  author={Arnol'd, Vladimir, I},
  journal={Mat. Zametki},
  volume={5},
  pages={227--231},
  year={1969}
}


%Barr
@article{barr,
  title={Harrison homology, {H}ochschild homology and triples},
  author={Barr, Michael},
  journal={Journal of Algebra},
  volume={8},
  number={3},
  pages={314--323},
  year={1968},
  publisher={Academic Press}
}


%Bergeron-Bergeron Type B
@article{Bergeron-Bergeron,
  title={Orthogonal idempotents in the descent algebra of {$B_n$} and applications},
  author={Bergeron, Fran{\c{c}}ois and Bergeron, Nantel},
  journal={Journal of Pure and Applied Algebra},
  volume={79},
  number={2},
  pages={109--129},
  year={1992},
  publisher={Elsevier}
}

@article{bergeron,
  title={Hyperoctahedral operations on {H}ochschild homology},
  author={Bergeron, Nantel},
  journal={Advances in Mathematics},
  volume={110},
  number={2},
  pages={255--276},
  year={1995},
  publisher={Elsevier}
}

@article{bergerondescent,
  title={A decomposition of the descent algebra of a finite {C}oxeter group},
  author={Bergeron, Fran{\c{c}}ois and Bergeron, Nantel and Howlett, Robert B and Taylor, Donald E},
  journal={Journal of Algebraic Combinatorics},
  volume={1},
  number={1},
  pages={23--44},
  year={1992},
  publisher={Springer}
}


%Berget zonotopal
@article{Berget,
  title={Internal zonotopal algebras and the monomial reflection groups},
  author={Berget, Andrew},
  journal={arXiv preprint arXiv:1611.06446},
  year={2016}
}

@article{Bremke,
  title={Reduced words and a length function for {$G (e, 1, n)$}},
  author={Bremke, Kirsten and Malle, Gunter},
  journal={Indagationes Mathematicae},
  volume={8},
  number={4},
  pages={453--469},
  year={1997},
  publisher={Elsevier}
}

@article{Bremke2,
  title={Root systems and length functions},
  author={Bremke, Kirsten and Malle, Gunter},
  journal={Geometriae Dedicata},
  volume={72},
  number={1},
  pages={83--97},
  year={1998},
  publisher={Springer}
}

@article{Casto,
  title={ {$\mathrm{ FI }_G $}-modules, orbit configuration spaces, and complex reflection groups},
  author={Casto, Kevin},
  journal={arXiv preprint arXiv:1608.06317},
  year={2016}
}

@article{chow2007descent,
  title={On the descent numbers and major indices for the hyperoctahedral group},
  author={Chow, Chak-On and Gessel, Ira M},
  journal={Advances in Applied Mathematics},
  volume={38},
  number={3},
  pages={275--301},
  year={2007},
  publisher={Elsevier}
}

@book{cohen,
  title={The homology of iterated loop spaces},
  author={Cohen, Frederick Ronald and Lada, Thomas Joseph and May, Peter J},
  volume={533},
  year={2007},
  publisher={Springer}
}


@article{diaconis2012foulkes,
  title={Foulkes characters, {E}ulerian idempotents, and an amazing matrix},
  author={Diaconis, Persi and Fulman, Jason},
  journal={Journal of Algebraic Combinatorics},
  volume={36},
  number={3},
  pages={425--440},
  year={2012},
  publisher={Springer}
}


%Early and Reiner, Configuration Spaces
@article{Early-Reiner,
  title={On configuration spaces and {W}hitehouse's lifts of the {E}ulerian representations},
  author={Early, Nicholas and Reiner, Victor},
  journal={Journal of Pure and Applied Algebra},
  year={2019},
  publisher={Elsevier}
}

@article{garsia,
  title={A decomposition of {S}olomon's descent algebra},
  author={Garsia, Adriano M and Reutenauer, Christophe},
  journal={Advances in Mathematics},
  volume={77},
  number={2},
  pages={189--262},
  year={1989},
  publisher={Elsevier}
}


%Gerstenhaber and Schack
@article{Gerstenhaber-Schack,
  title={A {H}odge-type decomposition for commutative algebra cohomology},
  author={Gerstenhaber, Murray and Schack, Samuel D},
  journal={Journal of Pure and Applied Algebra},
  volume={48},
  number={1-2},
  pages={229--247},
  year={1987},
  publisher={Elsevier}
}

@incollection{gerstenhaber2,
  title={Algebraic cohomology and deformation theory},
  author={Gerstenhaber, Murray and Schack, Samuel D},
  booktitle={Deformation theory of algebras and structures and applications},
  pages={11--264},
  year={1988},
  publisher={Springer}
}


@article{getzler1995cyclic,
  title={Cyclic operads and cyclic homology}, 
  journal= {Geometry, Topology and Physics for R. Bott, Conf. Proc. Lecture Notes Geom. Topology, IV},
  pages = {167--201},
  year={1995},
  author={Getzler, E and Kapranov, M},
  publisher={Intern. Press, Cambridge MA},
}

@article{Hanlon,
  title={The action of  {$ S_n $} on the components of the {H}odge decomposition of {H}ochschild homology.},
  author={Hanlon, Phil},
  journal={The Michigan Mathematical Journal},
  volume={37},
  number={1},
  pages={105--124},
  year={1990},
  publisher={The University of Michigan}
}
@article{hanlon-stanley,
  title={A {$q$}-deformation of a trivial symmetric group action},
  author={Hanlon, Phil and Stanley, Richard},
  journal={Transactions of the American Mathematical Society},
  volume={350},
  number={11},
  pages={4445--4459},
  year={1998}
}

@book{loday,
  title={Cyclic homology},
  author={Loday, Jean-Louis},
  volume={301},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{lodayoperations,
  title={Op{\'e}rations sur l'homologie cyclique des alg{\`e}bres commutatives},
  author={Loday, Jean-Louis},
  journal={Inventiones mathematicae},
  volume={96},
  number={1},
  pages={205--230},
  year={1989},
  publisher={Springer-Verlag}
}


@article{mathieu1996hidden,
  title={Hidden {$S_{n}$}-Actions},
  author={Mathieu, Olivier},
  journal={Commun. Math. Phys},
  volume={176},
  pages={467--474},
  year={1996},
  publisher={Springer}
}

@incollection{mathieu1995symplectic,
  title={The symplectic operad},
  author={Mathieu, Olivier},
  booktitle={Functional Analysis on the Eve of the 21st Century},
  pages={223--243},
  year={1995},
  publisher={Springer}
}


%Miller Foulkes
@article{Miller_Foulkes,
  title={Foulkes characters for complex reflection groups},
  author={Miller, Alexander},
  journal={Proceedings of the American Mathematical Society},
  volume={143},
  number={8},
  pages={3281--3293},
  year={2015}
}

@article{Miller-oral,
  title={Shephard groups and chamber geometry},
  author={Miller, Alexander},
  journal={Oral Exam Paper},
}

@article{Miller-thesis,
  title={Reflection arrangements and ribbon representations},
  author={Miller, Alexander},
  journal={PhD Thesis--University of Minnesota},
  year= {2013}
}

@article{millerreflection,
  title={Reflection arrangements and ribbon representations},
  author={Miller, Alexander R},
  journal={European Journal of Combinatorics},
  volume={39},
  pages={24--56},
  year={2014},
  publisher={Elsevier}
}



%Moynihan Colored idempotents
@article{Moynihan,
  title={The colored {E}ulerian descent algebra},
  author={Moynihan, Matthew},
  journal={Journal of Algebraic Combinatorics},
  volume={42},
  number={3},
  pages={671--694},
  year={2015},
  publisher={Springer}
}

@article{moseley-proudfoot-young,
  title={The {O}rlik-{T}erao algebra and the cohomology of configuration space},
  author={Moseley, Daniel and Proudfoot, Nicholas and Young, Ben},
  journal={Experimental Mathematics},
  volume={26},
  number={3},
  pages={373--380},
  year={2017},
  publisher={Taylor \& Francis}
}

%Orlike Reiner Shepler
@article{Orlik-Reiner-Shepler,
  title={The sign representation for {S}hephard groups},
  author={Orlik, Peter and Reiner, Victor and Shepler, Anne V},
  journal={Mathematische Annalen},
  volume={322},
  number={3},
  pages={477--492},
  year={2002},
  publisher={Springer}
}

@article{orlik-solomon,
  title={The {H}essian map in the invariant theory of reflection groups},
  author={Orlik, Peter and Solomon, Louis},
  journal={Nagoya Mathematical Journal},
  volume={109},
  pages={1--21},
  year={1988},
  publisher={Cambridge University Press}
}


@article{orlik-terao,
  title={Commutative algebras for arrangements},
  author={Orlik, Peter and Terao, Hiroaki},
  journal={Nagoya Mathematical Journal},
  volume={134},
  pages={65--73},
  year={1994},
  publisher={Cambridge University Press}
}

@article{reiner,
  title={The distribution of descents and length in a {C}oxeter group},
  author={Reiner, Victor},
  journal={The Electronic Journal of Combinatorics},
  volume={2},
  number={1},
  pages={25},
  year={1995}
}

@article{reiner2017non,
  title={On non-conjugate {C}oxeter elements in well-generated reflection groups},
  author={Reiner, Victor and Ripoll, Vivien and Stump, Christian},
  journal={Mathematische Zeitschrift},
  volume={285},
  number={3-4},
  pages={1041--1062},
  year={2017},
  publisher={Springer}
}

@article{solomon,
  title={A {M}ackey formula in the group ring of a {C}oxeter group},
  author={Solomon, Louis},
  journal={Journal of Algebra},
  volume={41},
  number={2},
  pages={255--264},
  year={1976},
  publisher={Academic Press}
}


@article{steingrimsson,
  title={Permutation statistics of indexed permutations},
  author={Steingr{\i}msson, Einar},
  journal={European Journal of Combinatorics},
  volume={15},
  number={2},
  pages={187--205},
  year={1994},
  publisher={Elsevier}
}

@article{sundaram1997,
  title={Group actions on arrangements of linear subspaces and applications to configuration spaces},
  author={Sundaram, Sheila and Welker, Volkmar},
  journal={Transactions of the American Mathematical Society},
  volume={349},
  number={4},
  pages={1389--1420},
  year={1997}
}

@article{sundaram1999,
  title={Homotopy of non-modular partitions and the {W}hitehouse module},
  author={Sundaram, Sheila},
  journal={Journal of Algebraic Combinatorics},
  volume={9},
  number={3},
  pages={251--269},
  year={1999},
  publisher={Springer}
}


@article{sundaram2018,
  title={On a curious variant of the $S_n$-module Lie$_n$},
  author={Sundaram, Sheila},
  journal={Algebraic Combinatorics},
  year={2020},
    pages = {985--1009},
     volume = {3},
     number = {4}
}


@article{varchenko1993bilinear,
  title={Bilinear form of real configuration of hyperplanes},
  author={Varchenko, Alexandre},
  journal={Adv. Math},
  volume={97},
  number={1},
  pages={110--144},
  year={1993}
}


@article{westerland,
  title={Configurations spaces via iterated fibrations},
  author={Westerland, Craig},
  journal={Notes for Topics in Topology: Weeks 2 and 3},
  year= {2015}
}

%Whitehouse
@article{Whitehouse,
  title={The {E}ulerian representations of {$\Sigma_{n}$} as restrictions of representations of {$\Sigma_{n+1}$}},
  author={Whitehouse, Sarah},
  journal={Journal of Pure and Applied Algebra},
  volume={115},
  number={3},
  pages={309--320},
  year={1997},
  publisher={Elsevier}
}

@article{wilson,
  title={Stability for hyperplane complements of type {$B/C$} and statistics on squarefree polynomials over finite fields},
  author={Rolland, Rita Jim{\'e}nez and Wilson, Jennifer CH},
  journal={arXiv preprint arXiv:1703.06349},
  year={2017}
}

@article{xico,
  title={Orbit configuration spaces, infinitesimal braid relations in homology and equivariant loop spaces.},
  author={Xicotencatl Merino, Miguel A},
  journal={PhD Thesis--University of Rochester.},
  year= {1997}
}

@article{moseley2017equivariant,
  title={Equivariant cohomology and the {V}archenko--{G}elfand filtration},
  author={Moseley, Daniel},
  journal={Journal of Algebra},
  volume={472},
  pages={95--114},
  year={2017},
  publisher={Elsevier}
}

@book{aguiarmahajan,
  title={Topics in hyperplane arrangements},
  author={Aguiar, Marcelo and Mahajan, Swapneel},
  volume={226},
  year={2017},
  publisher={American Mathematical Soc.}
}

@article{sundaramwelker,
  title={Group actions on arrangements of linear subspaces and applications to configuration spaces},
  author={Sundaram, Sheila and Welker, Volkmar},
  journal={Transactions of the American Mathematical Society},
  volume={349},
  number={4},
  pages={1389--1420},
  year={1997}
}

@article{BHR,
  title={A combinatorial description of the spectrum for the {T}setlin library and its generalization to hyperplane arrangements},
  author={Bidigare, Pat T and Hanlon, Phil and Rockmore, Dan},
  journal={Duke Mathematical Journal},
  volume={99},
  number={1},
  pages={135--174},
  year={1999},
  publisher={Citeseer}
}

@article{bidigare,
  title={Hyperplane arrangement face algebras and their associated {M}arkov chains},
  author={Bidigare, Patrick T},
    journal={PhD Thesis--University of Michigan},

  year={1998}
}

@article{RSW,
  title={Spectra of symmetrized shuffling operators},
  author={Reiner, Victor S and Saliola, Franco and Welker, Volkmar},
  journal={Memoirs of the American Mathematical Society},
  volume={228},
  number={1072},
  pages={1--121},
  year={2014},
  publisher={American Mathematical Society}
}


@incollection{goresky1988stratified,
  title={Stratified {M}orse theory},
  author={Goresky, Mark and MacPherson, Robert},
  booktitle={Stratified Morse Theory},
  pages={3--22},
  year={1988},
  publisher={Springer}
}

@article{hu1994homology,
  title={On the homology of complements of arrangements of subspaces and spheres},
  author={Hu, Yi},
  journal={Proceedings of the American Mathematical Society},
  volume={122},
  number={1},
  pages={285--290},
  year={1994}
}
@book{vasilev1994complements,
  title={Complements of discriminants of smooth maps: topology and applications},
  author={Vassiliev, Valeriui Aleksandrovich},
  volume={98},
  year={1994},
  publisher={American Mathematical Soc.}
}


@article{ziegler1991homotopy,
  title={Homotopy types of subspace arrangements via diagrams of spaces.},
  author={Ziegler, G{\"u}nter M and Zivaljevic, Rade T},
  journal={Mathematische Annalen},
  volume={295},
  number={3},
  pages={527--548},
  year={1993}
}


@book{orlikterao,
  title={Arrangements of hyperplanes},
  author={Orlik, Peter and Terao, Hiroaki},
  volume={300},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@article{cordovil2002commutative,
  title={A commutative algebra for oriented matroids},
  author={Cordovil, Raul},
  journal={Discrete \& Computational Geometry},
  volume={27},
  number={1},
  pages={73--84},
  year={2002},
  publisher={Springer}
}

@article{gelfand1989algebraic,
  title={Algebraic and topological invariants of oriented matroids},
  author={Gelfand, Israel M and Rybnikov, Grigori L},
  journal={Doklady Akademii Nauk SSSR},
  volume={307},
  number={4},
  pages={791--795},
  year={1989},
  publisher={MEZHDUNARODNAYA KNIGA 39 DIMITROVA UL., 113095 MOSCOW, RUSSIA}
}

@article{barcelo1995non,
  title={Non-broken circuits of reflection groups and factorization in ${D}_{n}$},
  author={Barcelo, H{\'e}l{\`e}ne and Goupil, Alain},
  journal={Israel Journal of Mathematics},
  volume={91},
  number={1-3},
  pages={285--306},
  year={1995},
  publisher={Springer}
}

@article{bergeron1995hyperoctahedral,
  title={Hyperoctahedral operations on {H}ochschild homology},
  author={Bergeron, Nantel},
  journal={Advances in Mathematics},
  volume={110},
  number={2},
  pages={255--276},
  year={1995},
  publisher={Elsevier}
}

@article{douglass2014cohomology,
  title={Cohomology of {C}oxeter arrangements and {S}olomon’s descent algebra},
  author={Douglass, J and Pfeiffer, G{\"o}tz and R{\"o}hrle, Gerhard},
  journal={Transactions of the American Mathematical Society},
  volume={366},
  number={10},
  pages={5379--5407},
  year={2014}
}

@article{reiner2019invariant,
  title={Invariant theory for coincidental complex reflection groups},
  author={Reiner, Victor and Shepler, Anne V and Sommers, Eric},
  journal={To appear in Math. Z.},
  year={2019}
}

@book{reutenauer2001free,
  title={Free {L}ie algebras},
  author={Reutenauer, Christophe},
  year={1993},
  volume={7},
  series = {London Mathematical Society Monographs. New Series},
  publisher={Oxford Science Publications. The Clarendon Press, Oxford University Press}
}

@incollection{garsia1990combinatorics,
  title={Combinatorics of the free {L}ie algebra and the symmetric group},
  author={Garsia, Adriano M},
  booktitle={Analysis, et cetera},
  pages={309--382},
  year={1990},
  publisher={Elsevier}
}

@incollection{joyal1986foncteurs,
  title={Foncteurs analytiques et especes de structures},
  author={Joyal, Andr{\'e}},
  booktitle={Combinatoire {\'e}num{\'e}rative},
  pages={126--159},
  year={1986},
  publisher={Spring-er}
}

@article{barcelo1990action,
  title={On the action of the symmetric group on the free {L}ie algebra and the partition lattice},
  author={Barcelo, H{\'e}l{\`e}ne},
  journal={Journal of Combinatorial Theory, Series A},
  volume={55},
  number={1},
  pages={93--129},
  year={1990},
  publisher={Elsevier}
}
@article{wachs1998co,
  title={On the (co) homology of the partition lattice and the free {L}ie algebra},
  author={Wachs, Michelle L},
  journal={Discrete Mathematics},
  volume={193},
  number={1-3},
  pages={287--319},
  year={1998},
  publisher={Elsevier}
}

@article{wachsdowling,
  title={Cohomology of {D}owling lattices and {L}ie (super)algebras},
  author={Wachs, Michelle L and Gottlieb, E. },
  journal={Advances in Applied Math},
  volume={24},
  number={4},
  pages={301-336},
  year={2000},
}

@book{tits1974buildings,
  title={Buildings of Spherical Type and Finite {B}{N}-Pairs},
  author={Tits, J},
  volume={386},
  year={1974},
  publisher={Springer Science \& Business Media}
}

@article{varchenkogelfand,
  title={Heaviside functions of a configuration of hyperplanes},
  author={Varchenko, A. N. and Gel{'}fand, I. M.  },
  journal={Funktsional Anal. i Prilozhen},
  volume={21},
  number={4},
  pages={1-18},
  year={1987},
}

@article{cellini1995general,
  title={A General Commutative Descent Algebra},
  author={Cellini, P},
  journal={Journal of Algebra},
  volume={3},
  number={175},
  pages={1015--1026},
  year={1995}
}


@article{petersen2020factorization,
  title={Factorization statistics and bug-eyed configuration spaces},
  author={Petersen, Dan and Tosteson, Philip},
  journal={arXiv preprint arXiv:2004.06024},
  year={2020}
}

@article{hyde,
    author = {Hyde, Trevor},
    title = "{Polynomial Factorization Statistics and Point Configurations in $\mathbb{R}^{3}$}",
    journal = {International Mathematics Research Notices},
    year = {2018},
    month = {12},
}

@article{abramenko1994walls,
  title={Walls in {C}oxeter complexes},
  author={Abramenko, Peter},
  journal={Geometriae Dedicata},
  volume={49},
  number={1},
  pages={71--84},
  year={1994},
  publisher={Springer}
}

@article{bjorner1992homology,
  title={The homology and shellability of matroids and geometric lattices},
  author={Bj{\"o}rner, Anders},
  journal={Matroid applications},
  volume={40},
  pages={226--283},
  year={1992}
}

@article{orlik1994commutative,
  title={Commutative algebras for arrangements},
  author={Orlik, Peter and Terao, Hiroaki},
  journal={Nagoya Mathematical Journal},
  volume={134},
  pages={65--73},
  year={1994},
  publisher={Cambridge University Press}
}

@article{barcelo1999lattices,
  title={Lattices of parabolic subgroups in connection with hyperplane arrangements},
  author={Barcelo, H{\'e}l{\`e}ne and Ihrig, Edwin},
  journal={Journal of Algebraic Combinatorics},
  volume={9},
  number={1},
  pages={5--24},
  year={1999},
  publisher={Springer}
}

@incollection{reutenauer1986theorem,
  title={Theorem of Poincar{\'e}-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to {S}tirling numbers},
  author={Reutenauer, Christophe},
  booktitle={Combinatoire {\'e}num{\'e}rative},
  pages={267--284},
  year={1986},
  publisher={Springer}
}

@article{bergeron1992decomposition,
  title={A decomposition of the descent algebra of a finite {C}oxeter group},
  author={Bergeron, Fran{\c{c}}ois and Bergeron, Nantel and Howlett, Robert B and Taylor, Donald E},
  journal={Journal of Algebraic Combinatorics},
  volume={1},
  number={1},
  pages={23--44},
  year={1992},
  publisher={Springer}
}

@article{saliola2009face,
  title={The face semigroup algebra of a hyperplane arrangement},
  author={Saliola, Franco V},
  journal={Canadian Journal of Mathematics},
  volume={61},
  number={4},
  pages={904--929},
  year={2009},
  publisher={Cambridge University Press}
}


@article{saliola2012eigenvectors,
  title={Eigenvectors for a random walk on a left-regular band},
  author={Saliola, Franco V},
  journal={Advances in Applied Mathematics},
  volume={48},
  number={2},
  pages={306--311},
  year={2012},
  publisher={Elsevier}
}

@article{sal2008quiv,
  title={On the quiver of the descent algebra},
  author={Saliola, Franco V},
  journal={Journal of Algebra},
  volume={320},
  number={11},
  pages={3866--3894},
  year={2008},
  publisher={Elsevier}
}

@article{saliolasemigroup,
title={The quiver of the semigroup algebra of a left regular band},
author={Saliola, Franco V},
journal={International Journal of Algebra and Computation},
volume={17},
number={8},
pages={1593--1610},
year={2007},
publisher={World Scientific}
}

@article{berg2011primitive,
  title={Primitive orthogonal idempotents for {R}-trivial monoids},
  author={Berg, Chris and Bergeron, Nantel and Bhargava, Sandeep and Saliola, Franco},
  journal={Journal of Algebra},
  volume={348},
  number={1},
  pages={446--461},
  year={2011},
  publisher={Elsevier}
}

@article{novelli2010representation,
  title={Representation theory of the higher-order peak algebras},
  author={Novelli, Jean-Christophe and Saliola, Franco and Thibon, Jean-Yves},
  journal={Journal of Algebraic Combinatorics},
  volume={32},
  number={4},
  pages={465--495},
  year={2010},
  publisher={Springer}
}

@article{hivert20111,
  title={The $(1-{E})$-transform in combinatorial {H}opf algebras},
  author={Hivert, Florent and Luque, Jean-Gabriel and Novelli, Jean-Christophe and Thibon, Jean-Yves},
  journal={Journal of Algebraic Combinatorics},
  volume={33},
  number={2},
  pages={277--312},
  year={2011},
  publisher={Springer}
}

@article{bergeron1991hyperoctahedrallie,
  title={A hyperoctahedral analogue of the free {L}ie algebra},
  author={Bergeron, Nantel},
  journal={Journal of Combinatorial Theory, Series A},
  volume={58},
  number={2},
  pages={256--278},
  year={1991},
  publisher={Elsevier}
}


@misc{brauner2020eulerian, 
AUTHOR = {Brauner, Sarah}, EPRINT = {2005.05953}, EPRINTTYPE = {arxiv}, TITLE = {Eulerian representations for real reflection groups}, YEAR = {2020}}