@misc {Ass-W,
    AUTHOR = {Assaf, S.},
     TITLE = {Weak dual equivalence for polynomials},
      Eprint = {1702.04051},
      Eprinttype = {arXiv},
      Year = {2017}
}

@article {Ass-H,
    AUTHOR = {Assaf, S.},
    TITLE = {Nonsymmetric {M}acdonald polynomials and a refinement of
              {K}ostka-{F}oulkes polynomials},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {370},
      YEAR = {2018},
    NUMBER = {12},
     PAGES = {8777--8796},
   MRCLASS = {33D52 (05E05)},
  MRNUMBER = {3864395},
       DOI = {10.1090/tran/7374},
}

@article {AS-D,
    AUTHOR = {Assaf, S. and Schilling, A.},
     TITLE = {A {D}emazure crystal construction for {S}chubert polynomials},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {1},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {225--247},
}

@article {AS17,
    AUTHOR = {Assaf, S. and Searles, D.},
     TITLE = {Schubert polynomials, slide polynomials, {S}tanley symmetric functions and quasi-{Y}amanouchi pipe dreams},
   JOURNAL = {Adv. in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {306},
      YEAR = {2017},
     PAGES = {89--122},
       DOI = {10.1016/j.aim.2016.10.015}
}

@article {AS18,
    AUTHOR = {Assaf, S. and Searles, D.},
     TITLE = {Kohnert tableaux and a lifting of quasi-{S}chur functions},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory, Series A},
    VOLUME = {156},
      YEAR = {2018},
     PAGES = {85--118},
       DOI = {10.1016/j.jcta.2018.01.001}
}

@unpublished {AG,
    AUTHOR = {Assaf, S. and Gonz\'{a}lez, N.S.},
     TITLE = {Demazure crystals for specialized nonsymmetric {M}acdonald polynomials},
      NOTE = {Preprint, forthcoming},
}

@article {Che95,
    AUTHOR = {Cherednik, Ivan},
     TITLE = {Nonsymmetric {M}acdonald polynomials},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1995},
    NUMBER = {10},
     PAGES = {483--515},
}

@article {Dem74a,
    AUTHOR = {Demazure, M.},
     TITLE = {D\'esingularisation des vari\'et\'es de {S}chubert g\'en\'eralis\'ees},
      NOTE = {Collection of articles dedicated to Henri Cartan on the
              occasion of his 70th birthday, I},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme
              S\'erie},
    VOLUME = {7},
      YEAR = {1974},
     PAGES = {53--88},
     URL = {http://www.numdam.org/item?id=ASENS_1974_4_7_1_53_0}
}

@article {Dem74,
    AUTHOR = {Demazure, M.},
     TITLE = {Une nouvelle formule des caract\`eres},
   JOURNAL = {Bull. Sci. Math. (2)},
  FJOURNAL = {Bulletin des Sciences Math\'ematiques. 2e S\'erie},
    VOLUME = {98},
      YEAR = {1974},
    NUMBER = {3},
     PAGES = {163--172},
}

@ARTICLE{GH93,
  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},
    VOLUME = {90},
      YEAR = {1993},
    NUMBER = {8},
     PAGES = {3607--3610},
   MRCLASS = {05E05 (05E10 20C30)},
  MRNUMBER = {1214091},
MRREVIEWER = {John R. Stembridge},
       DOI = {10.1073/pnas.90.8.3607},
}

@article {GH96,
    AUTHOR = {Garsia, A. M. and Haiman, M.},
     TITLE = {Some natural bigraded {$S_n$}-modules and {$q,t$}-{K}ostka
              coefficients},
      NOTE = {The Foata Festschrift},
   JOURNAL = {Electron. J. Combin.},
  FJOURNAL = {Electronic Journal of Combinatorics},
    VOLUME = {3},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {Research Paper 24, approx.\ 60 pp.},
}


@article {GP92,
    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},
   MRCLASS = {20C30 (05E10 05E35)},
  MRNUMBER = {1168926},
MRREVIEWER = {Leonid Krop},
       DOI = {10.1016/0001-8708(92)90034-I},
}

@article {Hag04,
    AUTHOR = {Haglund, J.},
     TITLE = {A combinatorial model for the {M}acdonald polynomials},
   JOURNAL = {Proc. Natl. Acad. Sci. USA},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {101},
      YEAR = {2004},
    NUMBER = {46},
     PAGES = {16127--16131},
       DOI = {10.1073/pnas.0405567101}
}

@article {HHL05,
    AUTHOR = {Haglund, J. and Haiman, M. and Loehr, N.},
     TITLE = {A combinatorial formula for {M}acdonald polynomials},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {18},
      YEAR = {2005},
    NUMBER = {3},
     PAGES = {735--761},
       DOI = {10.1090/S0894-0347-05-00485-6}
}

@article {HHL08,
    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},
       DOI = {10.1353/ajm.2008.0015}
}

@article {Hai01,
    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},
       DOI = {10.1090/S0894-0347-01-00373-3}
}

@article {Ion03,
    AUTHOR = {Ion, Bogdan},
     TITLE = {Nonsymmetric {M}acdonald polynomials and {D}emazure
              characters},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {116},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {299--318},
}


@article {Kas91,
    AUTHOR = {Kashiwara, M.},
     TITLE = {On crystal bases of the {$Q$}-analogue of universal enveloping
              algebras},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {63},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {465--516},
       DOI = {10.1215/S0012-7094-91-06321-0}
}

@article {Kas93,
    AUTHOR = {Kashiwara, M.},
     TITLE = {The crystal base and {L}ittelmann's refined {D}emazure
              character formula},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {71},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {839--858},
       DOI = {10.1215/S0012-7094-93-07131-1}
}

@article {KN94,
    AUTHOR = {Kashiwara, M. and Nakashima, T.},
     TITLE = {Crystal graphs for representations of the {$q$}-analogue of
              classical {L}ie algebras},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {165},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {295--345},
       DOI = {10.1006/jabr.1994.1114}
}

@article {Koh91,
    AUTHOR = {Kohnert, A.},
     TITLE = {Weintrauben, {P}olynome, {T}ableaux},
      NOTE = {Dissertation, Universit{\"a}t Bayreuth, Bayreuth, 1990},
   JOURNAL = {Bayreuth. Math. Schr.},
  FJOURNAL = {Bayreuther Mathematische Schriften},
    NUMBER = {38},
      YEAR = {1991},
     PAGES = {1--97},
}

@article {LS85,
    AUTHOR = {Lascoux, Alain and Sch\"utzenberger, Marcel-Paul},
     TITLE = {Schubert polynomials and the {L}ittlewood-{R}ichardson rule},
   JOURNAL = {Lett. Math. Phys.},
  FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid
              Dissemination of Short Contributions in the Field of
              Mathematical Physics},
    VOLUME = {10},
      YEAR = {1985},
    NUMBER = {2-3},
     PAGES = {111--124},
}


@incollection {LS90,
    AUTHOR = {Lascoux, Alain and Sch{\"u}tzenberger, Marcel-Paul},
     TITLE = {Keys \& standard bases},
 BOOKTITLE = {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)},
    SERIES = {IMA Vol. Math. Appl.},
    VOLUME = {19},
     PAGES = {125--144},
 PUBLISHER = {Springer, New York},
      YEAR = {1990},
}

@article {Lit95,
    AUTHOR = {Littelmann, P.},
     TITLE = {Crystal graphs and {Y}oung tableaux},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {175},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {65--87},
       DOI = {10.1006/jabr.1995.1175}
}

@ARTICLE{Mac88,
  author = {Macdonald, I.G.},
  title = {A new class of symmetric functions},
  journal = {Actes du 20e Seminaire Lotharingien},
  year = {1988},
  volume = {372},
  pages = {131--171},
}

@incollection {Mac91,
    AUTHOR = {Macdonald, I.G.},
     TITLE = {Notes on {S}chubert polynomials},
 PUBLISHER = {LACIM, Univ. Quebec a Montreal, Montreal, PQ},
      YEAR = {1991},
}

@incollection {Macdonald.1991,
    AUTHOR = {Macdonald, I.G.},
     TITLE = {Schubert polynomials},
 BOOKTITLE = {Surveys in combinatorics, 1991 ({G}uildford, 1991)},
    SERIES = {London Math. Soc. Lecture Note Ser.},
    VOLUME = {166},
     PAGES = {73--99},
 PUBLISHER = {Cambridge Univ. Press, Cambridge},
      YEAR = {1991},
}

@BOOK{Mac95,
  title = {Symmetric functions and {H}all polynomials},
  publisher = {The Clarendon Press Oxford University Press},
  year = {1995},
  author = {Macdonald, I.G.},
  series = {Oxford Mathematical Monographs},
  address = {New York},
  edition = {Second},
  note = {With contributions by A. Zelevinsky, Oxford Science Publications},
  pages = {x+475},
}

@article {Mac96,
    AUTHOR = {Macdonald, I.G.},
     TITLE = {Affine {H}ecke algebras and orthogonal polynomials},
      NOTE = {S\'eminaire Bourbaki, Vol. 1994/95},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {237},
      YEAR = {1996},
     PAGES = {Exp.\ No.\ 797, 4, 189--207},
}

@article {Mas09,
    AUTHOR = {Mason, S.},
     TITLE = {An explicit construction of type {A} {D}emazure atoms},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {29},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {295--313},
       DOI = {10.1007/s10801-008-0133-4}
}


@article {Opd95,
    AUTHOR = {Opdam, E.M.},
     TITLE = {Harmonic analysis for certain representations of graded
              {H}ecke algebras},
   JOURNAL = {Acta Math.},
  FJOURNAL = {Acta Mathematica},
    VOLUME = {175},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {75--121},
       DOI = {10.1007/BF02392487}
}

@article {RS95,
    AUTHOR = {Reiner, Victor and Shimozono, Mark},
     TITLE = {Key polynomials and a flagged {L}ittlewood-{R}ichardson rule},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {70},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {107--143},
}

@article {San00,
    AUTHOR = {Sanderson, Yasmine B.},
     TITLE = {On the connection between {M}acdonald polynomials and
              {D}emazure characters},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {11},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {269--275},
}