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@unpublished {Assaf,
    AUTHOR = {Assaf, Sami H.},
     TITLE = {An insertion algorithm for multiplying {D}emazure characters by {S}chur polynomials},
      NOTE = {arXiv:2109.05651},
}

@misc{ADG,
    AUTHOR = {Assaf, Sami and Dranowski, Anne and Gonz\'{a}lez, Nicolle},
     TITLE = {Extremal tensor products of {D}emazure crystals},
      eprint = {2210.10236},
}

@article {AG21,
    AUTHOR = {Assaf, Sami and Gonz\'{a}lez, Nicolle},
     TITLE = {Demazure crystals for specialized nonsymmetric {M}acdonald
              polynomials},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {182},
      YEAR = {2021},
     PAGES = {Paper No. 105463, 75},
}

@article {BGG73,
    AUTHOR = {Bernstein, I. N. and Gelfand, I. M. and Gelfand, S. I.},
     TITLE = {Schubert cells, and the cohomology of the spaces {$G/P$}},
   JOURNAL = {Uspehi Mat. Nauk},
  FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.
              Uspekhi Matematicheskikh Nauk},
    VOLUME = {28},
      YEAR = {1973},
    NUMBER = {3(171)},
     PAGES = {3--26},
}


@book {BB05,
    AUTHOR = {Bj\"{o}rner, Anders and Brenti, Francesco},
     TITLE = {Combinatorics of {C}oxeter groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {231},
 PUBLISHER = {Springer, New York},
      YEAR = {2005},
     PAGES = {xiv+363},
}

@article {Bor53,
    AUTHOR = {Borel, Armand},
     TITLE = {Sur la cohomologie des espaces fibr\'es principaux et des
              espaces homog\`enes de groupes de {L}ie compacts},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {57},
      YEAR = {1953},
     PAGES = {115--207},
}

@article {Dem74a,
    AUTHOR = {Demazure, Michel},
     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 {Dem74,
    AUTHOR = {Demazure, Michel},
     TITLE = {D\'esingularisation des vari\'et\'es de {S}chubert g\'en\'eralis\'ees},
   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},
}

@unpublished {DEKM,
    AUTHOR = {Dranowski, Anne and Elek, Balazs and Kamnitzer, Joel and Morton-Ferguson, Calder},
     TITLE = {Heaps, crystals, and preprojective algebra modules},
      NOTE = {arXiv:2202.02490},
}

@article {Gib21,
    AUTHOR = {Gibson, Joel},
     TITLE = {A {D}emazure character formula for the product monomial
              crystal},
   JOURNAL = {Algebr. Comb.},
  FJOURNAL = {Algebraic Combinatorics},
    VOLUME = {4},
      YEAR = {2021},
    NUMBER = {2},
     PAGES = {301--327},
}

@article {HLMvW11,
    AUTHOR = {Haglund, J. and Luoto, K. and Mason, S. and van Willigenburg,
              S.},
     TITLE = {Refinements of the {L}ittlewood-{R}ichardson rule},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {363},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {1665--1686},
}


@article {Ish15,
    AUTHOR = {Ishii, Motohiro},
     TITLE = {Demazure character formulas for generalized {K}ac-{M}oody
              algebras},
   JOURNAL = {Comm. Algebra},
  FJOURNAL = {Communications in Algebra},
    VOLUME = {43},
      YEAR = {2015},
    NUMBER = {7},
     PAGES = {2785--2801},
}

@article {Jos85,
    AUTHOR = {Joseph, A.},
     TITLE = {On the {D}emazure character formula},
   JOURNAL = {Ann. Sci. \'{E}cole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'{E}cole Normale Sup\'{e}rieure. Quatri\`eme
              S\'{e}rie},
    VOLUME = {18},
      YEAR = {1985},
    NUMBER = {3},
     PAGES = {389--419},
}

@article{Jos03,
  title={A decomposition theorem for Demazure crystals},
  author={Joseph, Anthony},
  journal={Journal of Algebra},
  volume={265},
  number={2},
  pages={562--578},
  year={2003},
  publisher={Academic Press}
}

@article{HK04,
  title={Crystals and coboundary categories},
  author={Andr'e G. Henriques and Joel Kamnitzer},
  journal={Duke Mathematical Journal},
  year={2004},
  volume={132},
  pages={191-216}
}



@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},
}

@article {Kas93,
    AUTHOR = {Kashiwara, Masaki},
     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},
}


@incollection {Kas94,
    AUTHOR = {Kashiwara, Masaki},
     TITLE = {On crystal bases},
 BOOKTITLE = {Representations of groups ({B}anff, {AB}, 1994)},
    SERIES = {CMS Conf. Proc.},
    VOLUME = {16},
     PAGES = {155--197},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {1995},
}

@article {Kou20,
    AUTHOR = {Kouno, Takafumi},
     TITLE = {Decomposition of tensor products of {D}emazure crystals},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {546},
      YEAR = {2020},
     PAGES = {641--678},
}

@article {KTWWY19,
    AUTHOR = {Kamnitzer, Joel and Tingley, Peter and Webster, Ben and
              Weekes, Alex and Yacobi, Oded},
     TITLE = {Highest weights for truncated shifted {Y}angians and product
              monomial crystals},
   JOURNAL = {J. Comb. Algebra},
  FJOURNAL = {Journal of Combinatorial Algebra},
    VOLUME = {3},
      YEAR = {2019},
    NUMBER = {3},
     PAGES = {237--303},
}

@article {LLM02,
    AUTHOR = {Lakshmibai, Venkatramani and Littelmann, Peter and Magyar,
              Peter},
     TITLE = {Standard monomial theory for {B}ott-{S}amel\-son varieties},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {130},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {293--318},
}

@article {LS19,
    AUTHOR = {Lenart, Cristian and Scrimshaw, Travis},
     TITLE = {On higher level {K}irillov-{R}eshetikhin crystals, {D}emazure
              crystals, and related uniform models},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {539},
      YEAR = {2019},
     PAGES = {285--304},
}

@article {Lit92,
    AUTHOR = {Littelmann, Peter},
     TITLE = {Good filtrations and decomposition rules for representations
              with standard monomial theory},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's
              Journal]},
    VOLUME = {433},
      YEAR = {1992},
     PAGES = {161--180},
}

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

@article {Lit95-2,
    AUTHOR = {Littelmann, Peter},
     TITLE = {Paths and root operators in representation theory},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {142},
      YEAR = {1995},
    NUMBER = {3},
     PAGES = {499--525},
}
		
@article {Lit94,
    AUTHOR = {Littelmann, Peter},
     TITLE = {A {L}ittlewood-{R}ichardson rule for symmetrizable
              {K}ac-{M}oody algebras},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {116},
      YEAR = {1994},
    NUMBER = {1-3},
     PAGES = {329--346},
}

@article {Lus90,
    AUTHOR = {Lusztig, G.},
     TITLE = {Canonical bases arising from quantized enveloping algebras},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {3},
      YEAR = {1990},
    NUMBER = {2},
     PAGES = {447--498},
}

@article {Mat89,
    AUTHOR = {Mathieu, Olivier},
     TITLE = {Filtrations of {$B$}-modules},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {59},
      YEAR = {1989},
    NUMBER = {2},
     PAGES = {421--442},
}

@article {Naoi12,
    AUTHOR = {Naoi, Katsuyuki},
     TITLE = {Weyl modules, {D}emazure modules and finite crystals for
              non-simply laced type},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {229},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {875--934},
}

@article {Naoi13,
    AUTHOR = {Naoi, Katsuyuki},
     TITLE = {Demazure crystals and tensor products of perfect
              {K}irillov-{R}eshetikhin crystals with various levels},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {374},
      YEAR = {2013},
     PAGES = {1--26},
}

@incollection {Pol89,
    AUTHOR = {Polo, Patrick},
     TITLE = {Vari\'{e}t\'{e}s de {S}chubert et excellentes filtrations},
      NOTE = {Orbites unipotentes et repr\'{e}sentations, III},
   JOURNAL = {Ast\'{e}risque},
  FJOURNAL = {Ast\'{e}risque},
    NUMBER = {173-174},
      YEAR = {1989},
     PAGES = {10--11, 281--311},
}

@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 {vdK89,
    AUTHOR = {van der Kallen, Wilberd},
     TITLE = {Longest weight vectors and excellent filtrations},
   JOURNAL = {Math. Z.},
  FJOURNAL = {Mathematische Zeitschrift},
    VOLUME = {201},
      YEAR = {1989},
    NUMBER = {1},
     PAGES = {19--31},
}


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