@article{HookBases,
  title={The Combinatorics of the Garsia-Haiman Modules for Hook Shapes},
  author={Ron M. Adin and Jeffrey B. Remmel and Yuval Roichman},
  journal={Electron. J. Comb.},
  year={2007},
  volume={15},
  NUMBER = {1},
       DOI = {10.37236/762},
       URL = {https://doi.org/10.37236/762},
}


@article{Alfano,
title = {A basis for the Y1 subspace of diagonal harmonic polynomials},
journal = {Discrete Mathematics},
volume = {193},
number = {1},
pages = {17-31},
year = {1998},
author = {Joseph Alfano}
}

@misc{CarlssonOblomkov,
  author = {Carlsson, Erik and Oblomkov, Alexei},
  
  title = {Affine Schubert calculus and double coinvariants},

   eprint = {1801.09033},
  archivePrefix = {arXiv},
  
  year = {2018}
}

@article{AllenOneVariable,
    AUTHOR = {Allen, Edward E.},
     TITLE = {A conjecture of {P}rocesi and the straightening algorithm of
              {R}ota},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {89},
      YEAR = {1992},
    NUMBER = {9},
     PAGES = {3980--3984}, 
       DOI = {10.1073/pnas.89.9.3980},
       URL = {https://doi.org/10.1073/pnas.89.9.3980},
}


@article{AllenBitableaux2,
  title={Bitableaux Bases for some Garsia-Haiman Modules and Other Related Modules},
  author={Edward E. Allen},
  journal={Electron. J. Comb.},
  year={2002},
  volume={9}
}

@article{AllenBitableaux1,
    AUTHOR = {Allen, Edward E.},
     TITLE = {Bitableaux bases for the diagonally invariant polynomial
              quotient rings},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {130},
      YEAR = {1997},
    NUMBER = {2},
     PAGES = {242--260}, 
       DOI = {10.1006/aima.1997.1652},
       URL = {https://doi.org/10.1006/aima.1997.1652},
}

@article{AllenDescentMonomials,
    AUTHOR = {Allen, E. E.},
     TITLE = {The descent monomials and a basis for the diagonally symmetric
              polynomials},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {3},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {5--16}, 
       DOI = {10.1023/A:1022481303750},
       URL = {https://doi.org/10.1023/A:1022481303750},
}

@article{HaimanGeometry,
    AUTHOR = {Haiman, Mark},
     TITLE = {Hilbert schemes, polygraphs and the {M}acdonald positivity
              conjecture},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {14},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {941--1006},
       DOI = {10.1090/S0894-0347-01-00373-3},
       URL = {https://doi.org/10.1090/S0894-0347-01-00373-3},
}


@article{HaimanDR,
    AUTHOR = {Haiman, Mark},
     TITLE = {Vanishing theorems and character formulas for the {H}ilbert
              scheme of points in the plane},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {149},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {371--407},
       DOI = {10.1007/s002220200219},
       URL = {https://doi.org/10.1007/s002220200219},
}

@book{Sagan,
    AUTHOR = {Sagan, Bruce E.},
     TITLE = {The symmetric group},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {203},
   EDITION = {Second},
      NOTE = {Representations, combinatorial algorithms, and symmetric
              functions},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2001},
     PAGES = {xvi+238},
       DOI = {10.1007/978-1-4757-6804-6},
       URL = {https://doi.org/10.1007/978-1-4757-6804-6},
}

@article{ATY,
    AUTHOR = {Ariki, Susumu and Terasoma, Tomohide and Yamada, Hiro-Fumi},
     TITLE = {Higher {S}pecht polynomials},
   JOURNAL = {Hiroshima Math. J.},
  FJOURNAL = {Hiroshima Mathematical Journal},
    VOLUME = {27},
      YEAR = {1997},
    NUMBER = {1},
     PAGES = {177--188}, 
       URL = {http://projecteuclid.org/euclid.hmj/1206127144},
}

@article{GillespieRhoades,
    AUTHOR = {Gillespie, M. and Rhoades, B.},
     TITLE = {Higher {S}pecht bases for generalizations of the coinvariant
              ring},
   JOURNAL = {Ann. Comb.},
  FJOURNAL = {Annals of Combinatorics},
    VOLUME = {25},
      YEAR = {2021},
    NUMBER = {1},
     PAGES = {51--77},
       DOI = {10.1007/s00026-020-00516-1},
       URL = {https://doi.org/10.1007/s00026-020-00516-1},
}

@article{Peel,
    AUTHOR = {Peel, M. H.},
     TITLE = {Specht modules and symmetric groups},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {36},
      YEAR = {1975},
    NUMBER = {1},
     PAGES = {88--97},
       DOI = {10.1016/0021-8693(75)90158-1},
       URL = {https://doi.org/10.1016/0021-8693(75)90158-1},
}


@article{HRS,
title = {Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture},
journal = {Adv. Math.},
volume = {329},
pages = {851--915},
year = {2018},
author = {James Haglund and Brendon Rhoades and Mark Shimozono},
       DOI = {10.1016/j.aim.2018.01.028},
       URL = {https://doi.org/10.1016/j.aim.2018.01.028},
}


@article{GarsiaProcesi,
    AUTHOR = {Garsia, A. M. and Procesi, C.},
     TITLE = {On certain graded {$S_n$}-modules and the {$q$}-{K}ostka
              polynomials},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {94},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {82--138}, 
       DOI = {10.1016/0001-8708(92)90034-I},
       URL = {https://doi.org/10.1016/0001-8708(92)90034-I},
}


@article{LascouxSchutzenberger,
 author = {Alain Lascoux and Marcel-Paul Sch\"{u}tzenberger}, 
 title = {Sur une conjecture de H. O. Foulkes.},
 journal = {C. R. Acad. Sci. Paris S\'er. I Math.},
 volume = {288},
 pages = {95–98}, 
 year = {1979}
}

@article{Stanley,
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Invariants of finite groups and their applications to
              combinatorics},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {1},
      YEAR = {1979},
    NUMBER = {3},
     PAGES = {475--511},
       DOI = {10.1090/S0273-0979-1979-14597-X},
       URL = {https://doi.org/10.1090/S0273-0979-1979-14597-X},
}

@article{DeConciniProcesi,
    AUTHOR = {De Concini, Corrado and Procesi, Claudio},
     TITLE = {Symmetric functions, conjugacy classes and the flag variety},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {64},
      YEAR = {1981},
    NUMBER = {2},
     PAGES = {203--219}, 
       DOI = {10.1007/BF01389168},
       URL = {https://doi.org/10.1007/BF01389168},
}

@article{Tanisaki,
    AUTHOR = {Tanisaki, Toshiyuki},
     TITLE = {Defining ideals of the closures of the conjugacy classes and
              representations of the {W}eyl groups},
   JOURNAL = {Tohoku Math. J. (2)},
  FJOURNAL = {The Tohoku Mathematical Journal. Second Series},
    VOLUME = {34},
      YEAR = {1982},
    NUMBER = {4},
     PAGES = {575--585},
       DOI = {10.2748/tmj/1178229158},
       URL = {https://doi.org/10.2748/tmj/1178229158},
}

@manual{sage,
  Key          = {SageMath},
  Author       = {{The Sage Developers}},
  Title        = {{S}ageMath ({V}ersion 9.0)},
  note         = {{\tt https://www.sagemath.org}},
  Year         = {2020},
}

@book{Macdonald,
    AUTHOR = {Macdonald, I. G.},
     TITLE = {Symmetric functions and {H}all polynomials},
    SERIES = {Oxford Mathematical Monographs},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {1979},
     PAGES = {viii+180},
}

@misc{garsiaZabrocki,
      title={A basis for the Diagonal Harmonic Alternants}, 
      author={Adriano Garsia and Mike Zabrocki},
      year={2022},
      eprint={2204.01812},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@book{Fulton,
    AUTHOR = {Fulton, William},
     TITLE = {Young tableaux},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {35},
      NOTE = {With applications to representation theory and geometry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1997},
     PAGES = {x+260}, 
MRREVIEWER = {Tadeusz\ J\'ozefiak},
}

@article{HHLRU,
    AUTHOR = {Haglund, J. and Haiman, M. and Loehr, N. and Remmel, J. B. and
              Ulyanov, A.},
     TITLE = {A combinatorial formula for the character of the diagonal
              coinvariants},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {126},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {195--232},
       DOI = {10.1215/S0012-7094-04-12621-1},
       URL = {https://doi.org/10.1215/S0012-7094-04-12621-1},
}

@article{shuffle,
    AUTHOR = {Carlsson, Erik and Mellit, Anton},
     TITLE = {A proof of the shuffle conjecture},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {31},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {661--697}, 
       DOI = {10.1090/jams/893},
       URL = {https://doi.org/10.1090/jams/893},
}

@article{Stembridge,
    AUTHOR = {Stembridge, John R.},
     TITLE = {Some particular entries of the two-parameter {K}ostka matrix},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {121},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {367--373},
       DOI = {10.2307/2160410},
       URL = {https://doi.org/10.2307/2160410},
}

@article{GillespieFull,
    AUTHOR = {Gillespie, Maria},
     TITLE = {Higher {S}pecht polynomials under the diagonal action},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {7},
      YEAR = {2024},
    NUMBER = {6},
     PAGES = {1731--1750},
       DOI = {10.5802/alco.396},
       URL = {https://doi.org/10.5802/alco.396},
}

@misc{Salois,
author = {K. Salois},
title = {Higher Specht bases and q-series for the cohomology rings of certain Hessenberg varieties},
      eprint={2410.08366},
      archivePrefix={arXiv},
year = {2024}
}

@article {StanleyStembridge,
    AUTHOR = {Stanley, Richard P. and Stembridge, John R.},
     TITLE = {On immanants of {J}acobi-{T}rudi matrices and permutations
              with restricted position},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {62},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {261--279},
       DOI = {10.1016/0097-3165(93)90048-D},
       URL = {https://doi.org/10.1016/0097-3165(93)90048-D},
}

@article{ShareshianWachs,
    AUTHOR = {Shareshian, John and Wachs, Michelle L.},
     TITLE = {Chromatic quasisymmetric functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {295},
      YEAR = {2016},
     PAGES = {497--551},
       DOI = {10.1016/j.aim.2015.12.018},
       URL = {https://doi.org/10.1016/j.aim.2015.12.018},
}

@misc{Hikita,
  author = {T. Hikita},
  title = {A proof of the Stanley--Stembridge conjecture},
  archivePrefix = {arXiV},
  eprint = {2410.12758},
year = {2024}
}