@Misc{Alexandersson16,
  author        = {P. Alexandersson},
  title         = {Non-symmetric Macdonald polynomials and Demazure-Lusztig operators},
  eprinttype    = {arxiv},
  year          = {2016},
  eprint        = {1602.05153},
}

@Article{AlexSawh19,
  author     = {Alexandersson, P. and Sawhney, M.},
  title      = {Properties of non-symmetric {M}acdonald polynomials at {$q=1$} and {$q=0$}},
  journal    = {Ann. Comb.},
  year       = {2019},
  volume     = {23},
  number     = {2},
  pages      = {219--239},
  issn       = {0218-0006},
  doi        = {10.1007/s00026-019-00432-z},
  fjournal   = {Annals of Combinatorics},
  mrclass    = {05E10 (05E05 20C08)},
  mrnumber   = {3962853},
  mrreviewer = {Elizabeth M. Niese},
}

@Article{AlexBrio05,
  author     = {Alexeev, V. and Brion, M.},
  title      = {Moduli of affine schemes with reductive group action},
  journal    = {J. Algebraic Geom.},
  year       = {2005},
  volume     = {14},
  number     = {1},
  pages      = {83--117},
  issn       = {1056-3911},
  fjournal   = {Journal of Algebraic Geometry},
  mrclass    = {14D22 (14C05 14M25 20G05)},
  mrnumber   = {2092127},
  mrreviewer = {I. Dolgachev},
}

@InCollection{BakDunFor00,
  author     = {Baker, T. H. and Dunkl, C. F. and Forrester, P. J.},
  title      = {Polynomial eigenfunctions of the {C}alogero-{S}utherland-{M}oser models with exchange terms},
  booktitle  = {Calogero-{M}oser-{S}utherland models ({M}ontr\'{e}al, {QC}, 1997)},
  publisher  = {Springer, New York},
  year       = {2000},
  series     = {CRM Ser. Math. Phys.},
  pages      = {37--51},
  mrclass    = {33C80 (33D80 81R12)},
  mrnumber   = {1843561},
  mrreviewer = {Patrick J. Moylan},
}

@Article{BeGaHaTe99,
  Title                    = {Identities and positivity conjectures for some remarkable operators in the theory of symmetric functions},
  Author                   = {Bergeron, F. and Garsia, A. M. and Haiman, M. and Tesler, G.},
  Journal                  = {Methods Appl. Anal.},
  Year                     = {1999},
  Note                     = {Dedicated to Richard A.\ Askey on the occasion of his 65th birthday, Part III},
  Number                   = {3},
  Pages                    = {363--420},
  Volume                   = {6},
  Fjournal                 = {Methods and Applications of Analysis},
  Mrclass                  = {05E05 (33D52)},
  Mrnumber                 = {MR1803316 (2002g:05184)},
  Mrreviewer               = {Ang{\`e}le M. Hamel}
}

@Article{BeGaSeXi16,
  Title                    = {Compositional {$(km,kn)$}-shuffle conjectures},
  Author                   = {Bergeron, F. and Garsia, A. and Sergel Leven, E.
 and Xin, Guoce},
  Journal                  = {Int. Math. Res. Not. IMRN},
  Year                     = {2016},
  Number                   = {14},
  Pages                    = {4229--4270},
  Fjournal                 = {International Mathematics Research Notices. IMRN},
  Mrclass                  = {05E05 (05E10)},
  Mrnumber                 = {3556418},
  Mrreviewer               = {Xinrong Ma}
}

@article{BHMPS-paths,
  title = {A shuffle theorem for paths under any line},
  author = {Blasiak, J. and Haiman, M. and Morse, J. and Pun, A. and Seelinger, G. H.},
  year = {2023/ed},
  journal = {Forum of Mathematics, Pi},
  volume = {11},
  pages = {e5},
  publisher = {{Cambridge University Press}},
  doi = {10.1017/fmp.2023.4},
  urldate = {2023-04-01},
  abstract = {We generalize the shuffle theorem and its (km,kn)(km,kn) version, as conjectured by Haglund et al. and Bergeron et al. and proven by Carlsson and Mellit, and Mellit, respectively. In our version the (km,kn)(km,kn) Dyck paths on the combinatorial side are replaced by lattice paths lying under a line segment whose x and y intercepts need not be integers, and the algebraic side is given either by a Schiffmann algebra operator formula or an equivalent explicit raising operator formula. We derive our combinatorial identity as the polynomial truncation of an identity of infinite series of GLl\textbackslash operatorname \{\textbackslash mathrm \{GL\}\}\_\{l\} characters, expressed in terms of infinite series versions of LLT polynomials. The series identity in question follows from a Cauchy identity for nonsymmetric Hall\textendash Littlewood polynomials.},
  langid = {english},
  keywords = {05E05,16T30},
}


@ARTICLE{BMPS2,
    AUTHOR = {Blasiak, J. and Morse, J. and Pun, A. and Summers,
              D.},
     TITLE = {{$k$}-{S}chur expansions of {C}atalan functions},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {371},
      YEAR = {2020},
     PAGES = {107209, 39},
   MRCLASS = {05E05 (14N35 33C52)},
  MRNUMBER = {4118771},
       DOI = {10.1016/j.aim.2020.107209},
}

@article{BHMPS-delta,
  title = {A {{Proof}} of the {{Extended Delta Conjecture}}},
  author = {Blasiak, J. and Haiman, M. and Morse, J. and Pun, A. and Seelinger, G. H.},
  year = {2023/ed},
  journal = {Forum of Mathematics, Pi},
  volume = {11},
  pages = {e6},
  publisher = {{Cambridge University Press}},
  doi = {10.1017/fmp.2023.3},
  urldate = {2023-04-01},
  abstract = {We prove the extended delta conjecture of Haglund, Remmel and Wilson, a combinatorial formula for {$\Delta$}hl{$\Delta{'}$}eken{$\Delta\Planckconst\mathsl{l}\Delta{'}\mathsl{e}\mathsl{k}\mathsl{e}\mathsl{n}\backslash$}Delta \_\{h\_l\}\textbackslash Delta ' \_\{e\_k\} e\_\{n\} , where {$\Delta{'}$}ek{$\Delta{'}\mathsl{e}\mathsl{k}\backslash$}Delta ' \_\{e\_k\} and {$\Delta$}hl{$\Delta\Planckconst\mathsl{l}\backslash$}Delta \_\{h\_l\} are Macdonald eigenoperators and en{$\mathsl{e}\mathsl{n}$}e\_n is an elementary symmetric function. We actually prove a stronger identity of infinite series of GLmGL{$\mathsl{m}\backslash$}operatorname \{\textbackslash mathrm \{GL\}\}\_m characters expressed in terms of LLT series. This is achieved through new results in the theory of the Schiffmann algebra and its action on the algebra of symmetric functions.},
  langid = {english},
  keywords = {05E05,16T30},
}

@misc{BHMPS-llt,
  title = {{{LLT}} Polynomials in the {{Schiffmann}} Algebra},
  author = {Blasiak, J. and Haiman, M. and Morse, J. and Pun, A. and Seelinger, G. H.},
  year = {2021},
  eprint = {2112.07063},
  eprinttype = {arxiv},
}

@misc{BHMPS-lw,
  title = {Dens, Nests and the {{Loehr-Warrington}} Conjecture},
  author = {Blasiak, J. and Haiman, M. and Morse, J. and Pun, A. and Seelinger, G. H.},
  year = 2021,
  eprint = {2112.07070},
  eprinttype = {arxiv},
}

@incollection {BroerNormality,
    AUTHOR = {Broer, B.},
     TITLE = {Normality of some nilpotent varieties and cohomology of line
              bundles on the cotangent bundle of the flag variety},
 BOOKTITLE = {Lie theory and geometry},
    SERIES = {Progr. Math.},
    VOLUME = {123},
     PAGES = {1--19},
 PUBLISHER = {Birkh\"auser Boston, Boston, MA},
      YEAR = {1994},
   MRCLASS = {14M17 (14M15 20G10)},
  MRNUMBER = {1327529},
MRREVIEWER = {H. H. Andersen},
       DOI = {10.1007/978-1-4612-0261-5_1},
}
 
                  
@Article{BurbSchi12,
  Title                    = {On the {H}all algebra of an elliptic curve, {I}},
  Author                   = {Burban, I. and Schiffmann, O.},
  Journal                  = {Duke Math. J.},
  Year                     = {2012},
  Number                   = {7},
  Pages                    = {1171--1231},
  Volume                   = {161},
  Fjournal                 = {Duke Mathematical Journal},
  Mrclass                  = {16T05 (14F05)},
  Mrnumber                 = {2922373},
  Mrreviewer               = {Shilin Yang}
}

@Article{CarlMell18,
  Title                    = {A proof of the shuffle conjecture},
  Author                   = {Carlsson, E. and Mellit, A.},
  Journal                  = {J. Amer. Math. Soc.},
  Year                     = {2018},
  Number                   = {3},
  Pages                    = {661--697},
  Volume                   = {31},
  Fjournal                 = {Journal of the American Mathematical Society},
  Mrclass                  = {05E10 (05E05 33D52)},
  Mrnumber                 = {3787405},
  Mrreviewer               = {Tanja Stojadinovi\'{c}}
}
                  
@article{DaddMell22,
  title = {A Proof of the Compositional {{Delta}} Conjecture},
  author = {D'Adderio, M. and Mellit, A.},
  year = 2022,
  month = {jun},
  journal = {Advances in Mathematics},
  volume = 402,
  pages = 108342,
  issn = {0001-8708},
  abstract = {We prove a compositional refinement of the Delta conjecture (rise version) of Haglund, Remmel and Wilson [16] for {$\Delta$}en-k-1{${'}$}en which was stated in [8] in terms of Theta operators.},
  langid = {english},
  keywords = {Delta conjecture,Dyck path algebra,Macdonald polynomials,Theta operators},
  file = {/Users/ghseeli/Dropbox (University of Michigan)/pdfs/dadderioProofCompositionalDelta2022.pdf;/Users/ghseeli/Zotero/storage/P9VSCFGY/S000187082200158X.html},
}


@Article{DescLasc07,
  author   = {Descouens, F. and Lascoux, A.},
  title    = {Non-symmetric {H}all-{L}ittlewood polynomials},
  journal  = {S\'{e}m. Lothar. Combin.},
  year     = {2005/07},
  volume   = {54A},
  pages    = {Art. B54Ar, 14},
  fjournal = {S\'{e}minaire Lotharingien de Combinatoire},
  groups   = {Schiffman stuff},
  mrclass  = {05E05 (20C08)},
  mrnumber = {2264938},
}
                  
@Article{FeHaHoShYa09,
  author     = {Feigin, B. and Hashizume, K. and Hoshino, A. and Shiraishi, J. and Yanagida, S.},
  title      = {A commutative algebra on degenerate {$\Bbb{CP}^1$} and {M}acdonald polynomials},
  journal    = {J. Math. Phys.},
  year       = {2009},
  volume     = {50},
  number     = {9},
  pages      = {095215, 42},
  issn       = {0022-2488},
  fjournal   = {Journal of Mathematical Physics},
  mrclass    = {33D80 (33D52)},
  mrnumber   = {2566895},
  mrreviewer = {Erik Koelink},
}

@Article{FeigTsym11,
  Title                    = {Equivariant {$K$}-theory of {H}ilbert schemes via shuffle algebra},
  Author                   = {Feigin, B. L. and Tsymbaliuk, A. I.},
  Journal                  = {Kyoto J. Math.},
  Year                     = {2011},
  Number                   = {4},
  Pages                    = {831--854},
  Volume                   = {51},
  Fjournal                 = {Kyoto Journal of Mathematics},
  Mrclass                  = {14C35 (14C05 17B67 17B69 19E99)},
  Mrnumber                 = {2854154 (2012m:14018)},
  Mrreviewer               = {Guillermo Corti{\~n}as}
}

@article {FuLascouxkernel,
    AUTHOR = {Fu, A. M. and Lascoux, A.},
     TITLE = {Non-symmetric {C}auchy kernels for the classical groups},
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    VOLUME = {116},
      YEAR = {2009},
    NUMBER = {4},
     PAGES = {903--917},
     CODEN = {JCBTA7},
   MRCLASS = {05E15},
  MRNUMBER = {2513641 (2010f:05190)},
       DOI = {10.1016/j.jcta.2008.10.007},
}

@article {GarsiaHaiman93,
    AUTHOR = {Garsia, A. M. and Haiman, M.},
     TITLE = {A graded representation model for {M}acdonald's polynomials},
   JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
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    NUMBER = {8},
     PAGES = {3607--3610},
     CODEN = {PNASA6},
   MRCLASS = {05E05 (05E10 20C30)},
  MRNUMBER = {1214091},
MRREVIEWER = {John R. Stembridge},
}


@article {GaHa96,
   AUTHOR = {Garsia, A. M. and Haiman, M.},
    TITLE = {A remarkable $q,t$-{C}atalan sequence and $q$-{L}agrange
             inversion},
  JOURNAL = {J. Algebraic Combin.},
 FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
   VOLUME = {5},
     YEAR = {1996},
   NUMBER = {3},
    PAGES = {191--244},
    CODEN = {JAOME7},
}

@Article{GarsHaim96,
  Title                    = {Some natural bigraded {$S\sb n$}-modules and {$q,t$}-{K}ostka coefficients},
  Author                   = {Garsia, A. M. and Haiman, M.},
  Journal                  = {Electron. J. Combin.},
  Year                     = {1996},
  Note                     = {The Foata Festschrift},
  Number                   = {2},
  Pages                    = {Research Paper 24, approx.\ 60 pp.\ (electronic)},
  Volume                   = {3},
  Fjournal                 = {Electronic Journal of Combinatorics},
  Mrclass                  = {05E10 (05E05)},
  Mrnumber                 = {MR1392509 (97k:05205)},
  Mrreviewer               = {Edward E. Allen},
}

@Article{GaHaTe99,
  Title                    = {Explicit plethystic formulas for {M}acdonald {$q,t$}-{K}ostka coefficients},
  Author                   = {Garsia, A. M. and Haiman, M. and Tesler, G.},
  Journal                  = {S\'em. Lothar. Combin.},
  Year                     = {1999},
  Note                     = {The Andrews Festschrift (Maratea, 1998)},
  Pages                    = {Art. B42m, 45 pp. (electronic)},
  Volume                   = {42},
  Fjournal                 = {S\'eminaire Lotharingien de Combinatoire},
  Mrclass                  = {05E05 (33D52)},
  Mrnumber                 = {MR1701592 (2001b:05222)},
  Mrreviewer               = {Yasmine B. Sanderson},
}

@article {GHRS,
    AUTHOR = {Gorsky, E. and Hawkes, G. and Schilling, A. and
              Rainbolt, J.},
     TITLE = {Generalized {$q, t$}-{C}atalan numbers},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {3},
      YEAR = {2020},
    NUMBER = {4},
     PAGES = {855--886},
   MRCLASS = {05A15},
  MRNUMBER = {4145982},
       DOI = {10.5802/alco.120},
       URL = {https://doi.org/10.5802/alco.120},
}


@Unpublished{GrojHaim07,
  author    = {Grojnowski, I. and Haiman, M.},
  title     = {Affine {H}ecke algebras and positivity of {LLT} and {M}acdonald polynomials},
  note      = {Unpublished manuscript},
  year      = {2007},
}

@Article{HaHaLo05,
  Title                    = {A combinatorial formula for {M}acdonald polynomials},
  Author                   = {Haglund, J. and Haiman, M. and Loehr, N.},
  Journal                  = {J. Amer. Math. Soc.},
  Year                     = {2005},
  Number                   = {3},
  Pages                    = {735--761 (electronic)},
  Volume                   = {18},
  Mrclass                  = {05E05},
  Mrnumber                 = {MR2138143 (2006g:05223a)},
  Mrreviewer               = {Frank Sottile}
}

@article {HaHaLo08,
    AUTHOR = {Haglund, J. and Haiman, M. and Loehr, N.},
     TITLE = {A combinatorial formula for nonsymmetric {M}acdonald
              polynomials},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {130},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {359--383},
   MRCLASS = {05E05},
  MRNUMBER = {2405160},
MRREVIEWER = {Pavlo Pylyavskyy},
       DOI = {10.1353/ajm.2008.0015},
}

@Article{HaHaLoReUl05,
  Title                    = {A combinatorial formula for the character of the diagonal coinvariants},
  Author                   = {Haglund, J. and Haiman, M. and Loehr, N. and Remmel, J. B. and Ulyanov, A.},
  Journal                  = {Duke Math. J.},
  Year                     = {2005},
  Number                   = {2},
  Pages                    = {195--232},
  Volume                   = {126},
  Coden                    = {DUMJAO},
  Fjournal                 = {Duke Mathematical Journal},
  Mrclass                  = {05E10 (05A30 20C30)},
  Mrnumber                 = {MR2115257 (2006f:05186)},
  Mrreviewer               = {Edward E. Allen}
}

@Article{HagMoZa12,
  author     = {Haglund, J. and Morse, J. and Zabrocki, M.},
  title      = {A compositional shuffle conjecture specifying touch points of the {D}yck path},
  journal    = {Canad. J. Math.},
  year       = {2012},
  volume     = {64},
  number     = {4},
  pages      = {822--844},
  issn       = {0008-414X},
  fjournal   = {Canadian Journal of Mathematics. Journal Canadien de Math\'{e}matiques},
  mrclass    = {05E05 (33D52)},
  mrnumber   = {2957232},
  mrreviewer = {Arthur L. B. Yang}
}

@Article{HagRemWil18,
  author     = {Haglund, J. and Remmel, J. B. and Wilson, A. T.},
  title      = {The delta conjecture},
  journal    = {Trans. Amer. Math. Soc.},
  year       = {2018},
  volume     = {370},
  number     = {6},
  pages      = {4029--4057},
  issn       = {0002-9947},
  fjournal   = {Transactions of the American Mathematical Society},
  mrclass    = {05E05},
  mrnumber   = {3811519},
  mrreviewer = {David J. Grabiner},
}

@InCollection{Haiman99,
  author    = {Haiman, M.},
  title     = {Macdonald polynomials and geometry},
  booktitle = {New perspectives in algebraic combinatorics (Berkeley, CA, 1996--97)},
  publisher = {Cambridge Univ. Press},
  year      = {1999},
  volume    = {38},
  series    = {Math. Sci. Res. Inst. Publ.},
  pages     = {207--254},
  address   = {Cambridge},
  mrclass   = {05E05 (14C05)},
  mrnumber  = {MR1731818 (2001k:05203)},
}

@article {Haiman01,
    AUTHOR = {Haiman, M.},
     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 (electronic)},
   MRCLASS = {14C05 (05E05 20C30 33D45)},
  MRNUMBER = {1839919 (2002c:14008)},
MRREVIEWER = {Claudio Procesi},
}

@Article{Haiman02,
  Title                    = {Vanishing theorems and character formulas for the {H}ilbert scheme of points in the plane},
  Author                   = {Haiman, M.},
  Journal                  = {Invent. Math.},
  Year                     = {2002},
  Number                   = {2},
  Pages                    = {371--407},
  Volume                   = {149},
  Coden                    = {INVMBH},
  Fjournal                 = {Inventiones Mathematicae},
  Mrclass                  = {14C05 (05E05 14F17 14R20)},
  Mrnumber                 = {MR1918676 (2003f:14006)},
  Mrreviewer               = {Claudio Procesi}
}

@Article{Hikita14,
  author     = {Hikita, T.},
  title      = {Affine {S}pringer fibers of type {$A$} and combinatorics of diagonal coinvariants},
  journal    = {Adv. Math.},
  year       = {2014},
  volume     = {263},
  pages      = {88--122},
  issn       = {0001-8708},
  fjournal   = {Advances in Mathematics},
  mrclass    = {14L35 (05Exx)},
  mrnumber   = {3239135},
  mrreviewer = {Anthony Henderson}
}

@Article{Ion03,
  author     = {Ion, B.},
  title      = {Nonsymmetric {M}acdonald polynomials and {D}emazure characters},
  journal    = {Duke Math. J.},
  year       = {2003},
  volume     = {116},
  number     = {2},
  pages      = {299--318},
  issn       = {0012-7094},
  coden      = {DUMJAO},
  fjournal   = {Duke Mathematical Journal},
  groups     = {DAHA, Macdonald pols},
  mrclass    = {33D52 (17B67 33D45)},
  mrnumber   = {MR1953294 (2004d:33019)},
  mrreviewer = {Laurent Habsieger},
}

@Article{Ion08,
  author   = {Ion, B.},
  title    = {Standard bases for affine parabolic modules and nonsymmetric {M}acdonald polynomials},
  journal  = {J. Algebra},
  year     = {2008},
  volume   = {319},
  number   = {8},
  pages    = {3480--3517},
  issn     = {0021-8693},
  fjournal = {Journal of Algebra},
  mrclass  = {20C08 (05E05 33C52 33D52)},
  mrnumber = {2408328},
}

@Article{Jing94,
  author     = {Jing, N. H.},
  title      = {{$q$}-hypergeometric series and {M}acdonald functions},
  journal    = {J. Algebraic Combin.},
  year       = {1994},
  volume     = {3},
  number     = {3},
  pages      = {291--305},
  issn       = {0925-9899},
  fjournal   = {Journal of Algebraic Combinatorics. An International Journal},
  mrclass    = {33D15 (05A30 05E05 33D45)},
  mrnumber   = {1285498},
  mrreviewer = {Laurent Habsieger},
}

@Article{JJ92,
  author     = {Jing, N. and Jozefiak, T.},
  title      = {A formula for two-row Macdonald functions},
  journal    = {Duke Math. J.},
  year       = {1992},
  volume     = {67},
  number     = {2},
  pages      ={ 377-385},
  }

@incollection {Lascouxdoublecrystal,
    AUTHOR = {Lascoux, A.},
     TITLE = {Double crystal graphs},
 BOOKTITLE = {Studies in memory of {I}ssai {S}chur ({C}hevaleret/{R}ehovot,
              2000)},
    SERIES = {Progr. Math.},
    VOLUME = {210},
     PAGES = {95--114},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {2003},
   MRCLASS = {05E05 (17B10)},
  MRNUMBER = {1985724 (2004f:05186)},
MRREVIEWER = {Rosa C. Orellana},
}


@Article{LaLeTh97,
  author     = {Lascoux, A. and Leclerc, B. and Thibon, J.-Y.},
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  number     = {2},
  pages      = {1041--1068},
  issn       = {0022-2488},
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  mrclass    = {05E10 (05E05 33D80 81R10)},
  mrnumber   = {MR1434225 (98c:05167)},
  mrreviewer = {Thomas Scharf},
}

@article {LassalleSchlosser06,
    AUTHOR = {Lassalle, M. and Schlosser, M.},
     TITLE = {Inversion of the {P}ieri formula for {M}acdonald polynomials},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {202},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {289--325},
   MRCLASS = {05E05},
  MRNUMBER = {2222355},
MRREVIEWER = {Thomas Fun Yau Lam},
       DOI = {10.1016/j.aim.2005.03.009},
}
                  
@Article{LoehWarr08,
  author     = {Loehr, N. A. and Warrington, G. S.},
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  year       = {2008},
  number     = {5},
  pages      = {Art. ID rnm 157, 29},
  issn       = {1073-7928},
  fjournal   = {International Mathematics Research Notices. IMRN},
  mrclass    = {05E05},
  mrnumber   = {2418288},
  mrreviewer = {Eric S. Egge},
}
                  
@Article{Lusztig85,
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  journal    = {Proc. Amer. Math. Soc.},
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