% This is an example bibliography file for FPSAC submissions.

@article{LNSSS3,
    AUTHOR = {Lenart, C. and Naito, S. and Sagaki, D. and Schilling, A. and
              Shimozono, M.},
     TITLE = {A uniform model for {K}irillov-{R}eshetikhin crystals {III}:
              nonsymmetric {M}acdonald polynomials at {$t=0$} and {D}emazure
              characters},
   JOURNAL = {Transform. Groups},
  FJOURNAL = {Transformation Groups},
    VOLUME = {22},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {1041--1079}, 
       DOI = {10.1007/s00031-017-9421-1},
       URL = {https://doi.org/10.1007/s00031-017-9421-1},
}

@article{LNSSS2,
    AUTHOR = {Lenart, Cristian and Naito, Satoshi and Sagaki, Daisuke and
              Schilling, Anne and Shimozono, Mark},
     TITLE = {A uniform model for {K}irillov-{R}eshetikhin crystals {II}.
              {A}lcove model, path model, and {$P=X$}},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2017},
    NUMBER = {14},
     PAGES = {4259--4319}, 
       DOI = {10.1093/imrn/rnw129},
       URL = {https://doi.org/10.1093/imrn/rnw129},
}

@article{10.1215/S0012-7094-91-06321-0,
author = {M. Kashiwara},
title = {{On crystal bases of the $Q$-analogue of universal enveloping algebras}},
volume = {63},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
number = {2},
pages = {465-516},
year = {1991},
doi = {10.1215/S0012-7094-91-06321-0},
}

@article{Macdonald1988,
author = {Macdonald, I.G.},
journal = {Sém. Lothar. Combin.},
keywords = {Jack symmetric functions; Schur functions; Hall-Littlewood functions},
pages = {131-172},
title = {A new class of symmetric functions.},
url = {http://eudml.org/doc/120965},
volume = {20},
year = {1988},
}

@article{LP, 
 abstract = {We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a Littlewood-Richardson rule for decomposing tensor products of irreducible representations. The new model is based on the notion of a λ-chain, which is a chain of positive roots defined by certain interlacing conditions.},
 author = {Lenart, C. and Postnikov, A.},
 journal = {Trans.  Amer. Math. Soc.},
 number = {8},
 pages = {4349--4381},
 publisher = {American Mathematical Society},
 title = {A combinatorial model for crystals of Kac-Moody algebras},
 volume = {360},
 year = {2008},
       DOI = {10.1090/S0002-9947-08-04419-X},
}

@article{Assaf2018,
    AUTHOR = {Assaf, Sami},
     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}, 
       DOI = {10.1090/tran/7374}, 
}
@article{lenart2015generalization,
    AUTHOR = {Lenart, Cristian and Lubovsky, Arthur},
     TITLE = {A generalization of the alcove model and its applications},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {41},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {751--783}, 
       DOI = {10.1007/s10801-014-0552-3},
       URL = {https://doi.org/10.1007/s10801-014-0552-3},
}

@article{Kirillov1990RepresentationsOY,
  title={Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras},
  author={Kirillov, A. and Reshetikhin, N.},
    journal={J. Sov. Math.},
  fjournal={Journal of Soviet Mathematics},
  year={1990},
  volume={52},
  number = {3},
  pages={3156--3164},
  doi = {10.1007/BF02342935},
}

@article{Haglund_2004,
	doi = {10.1073/pnas.0405567101},  
	year = {2004},
	volume = {101},
	number = {46},
	pages = {16127-16131},
	author = {Haglund, J.},
	title = {A combinatorial model for the Macdonald polynomials},
    journal={Proc. Natl. Acad. Sci. USA},
	fjournal = {Proceedings of the National Academy of Sciences}
}

@article{HHLnonsymm,
 URL = {http://www.jstor.org/stable/40068131},
 abstract = {We give a combinatorial formula for the nonsymmetric Macdonald polynomials Eµ(x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials $J_\mu \,(x;\,q,\,t)$ . We prove the new formula by verifying that it satisfies a recurrence, due to Knop and Sahi, that characterizes the nonsymmetric Macdonald polynomials.},
 author = {Haglund, J. and Haiman, M. and Loehr, N.},
 journal = {Amer. J. Math.},
 number = {2},
 pages = {359-383},
 title = {A combinatorial formula for nonsymmetric Macdonald polynomials},
 volume = {130},
 year = {2008}
}

@article{ASSAF2021105463,
title = {Demazure crystals for specialized nonsymmetric Macdonald polynomials},
journal = {J. of Comb. Theory, Ser. {A}},
volume = {182},
year = {2021},
doi = {https://doi.org/10.1016/j.jcta.2021.105463},
author = {Assaf, S. and González, N.},
keywords = {Demazure crystal, Demazure character, Nonsymmetric Macdonald polynomial, Hall–Littlewood polynomial, Kostka–Foulkes polynomial},
abstract = {We give an explicit, nonnegative formula for the expansion of nonsymmetric Macdonald polynomials specialized at t=0 in terms of Demazure characters. Our formula results from constructing Demazure crystals whose characters are the nonsymmetric Macdonald polynomials, which also gives a new proof that these specialized nonsymmetric Macdonald polynomials are positive graded sums of Demazure characters. Demazure crystals are certain truncations of classical crystals that give a combinatorial skeleton for Demazure modules. To prove our construction, we develop further properties of Demazure crystals, including an efficient algorithm for computing their characters from highest weight elements. As a corollary, we obtain a new formula for the Schur expansion of Hall–Littlewood polynomials in terms of a simple statistic on highest weight elements of our crystals.}
}

@article{RAM2011309,
title = {A combinatorial formula for Macdonald polynomials},
journal = {Adv. Math.},
volume = {226},
number = {1},
pages = {309-331},
year = {2011},
doi = {https://doi.org/10.1016/j.aim.2010.06.022},
author = {Ram, A. and Yip, M.},
keywords = {Macdonald polynomials, Symmetric functions, Path model, Alcove walks, Combinatorial formulas},
}

@book{hongintroduction,
    AUTHOR = {Hong, Jin and Kang, Seok-Jin},
     TITLE = {Introduction to quantum groups and crystal bases},
    SERIES = {Grad. Stud. Math.},
    VOLUME = {42},
 PUBLISHER = {American Mathematical Society, {Providence, RI}},
      YEAR = {2002},
     PAGES = {xviii+307 pp.}, 
       DOI = {10.1090/gsm/042},
       URL = {https://doi.org/10.1090/gsm/042},
}


@article{RamGuo,
    author = {Guo, W. and Ram, A.},
    title = {Comparing formulas for type $GL_n$ Macdonald polynomials},
    journal = {Algebr. Comb.},
    volume = {5},
    number = {5},
    pages = {849-883},
    year = {2022},
    doi = {10.5802/alco.227}
}

@article{Assaf_2021,
	doi = {10.5802/alco.178},
	year = 2021,
	volume = {4},
	number = {5},
	pages = {777--793},
	author = {Assaf, S. and Gonz{\'{a}}lez, N.},
	title = {Affine Demazure crystals for specialized nonsymmetric Macdonald polynomials},
	journal = {Alg. Comb.}
}

@article{FOURIER2007386,
title = {Demazure structure inside Kirillov--Re\-she\-ti\-khin crystals},
journal = {J. Algebra},
volume = {309},
number = {1},
pages = {386-404},
year = {2007},
doi = {https://doi.org/10.1016/j.jalgebra.2006.09.019},
author = {Fourier, G. and Schilling, A. and Shimozono, M.},
keywords = {Quantum affine algebras, Crystal bases, Demazure crystals, Kirillov–Reshetikhin crystals},
abstract = {The conjecturally perfect Kirillov–Reshetikhin (KR) crystals are known to be isomorphic as classical crystals to certain Demazure subcrystals of crystal graphs of irreducible highest weight modules over affine algebras. Under some assumptions we show that the classical isomorphism from the Demazure crystal to the KR crystal, sends zero arrows to zero arrows. This implies that the affine crystal structure on these KR crystals is unique.}
}

@book {macaha,
    AUTHOR = {Macdonald, I. G.},
     TITLE = {Affine {H}ecke algebras and orthogonal polynomials},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {157},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2003},
     PAGES = {x+175 pp.}, 
       DOI = {10.1017/CBO9780511542824},
       URL = {https://doi.org/10.1017/CBO9780511542824},
}

@article{lascma,
author={Briggs, C. and Lenart, C. and Schultze, A.},
title={On combinatorial models for affine crystals},
eprint= {2109.12199},
journal = {S\'{e}m. Lothar. Combin. },
volume = {85B},
pages = {Art. 20, 13 pp.},
year = {2021},
}

@article{bmpdcs,
    AUTHOR = {Blasiak, Jonah and Morse, Jennifer and Pun, Anna},
     TITLE = {Demazure crystals and the {S}chur positivity of {C}atalan
              functions},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {236},
      YEAR = {2024},
    NUMBER = {2},
     PAGES = {483--547}, 
       DOI = {10.1007/s00222-024-01237-5},
       URL = {https://doi.org/10.1007/s00222-024-01237-5},
}

@article {kancgr,
    AUTHOR = {Kashiwara, Masaki and Nakashima, Toshiki},
     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},
       URL = {https://doi.org/10.1006/jabr.1994.1114},
}

@book {hkorff,
    AUTHOR = {Hatayama, G. and Kuniba, A. and Okado, M. and Takagi, T. and
             Yamada, Y.},
     TITLE = {Remarks on fermionic formula},
 BOOKTITLE = {Recent developments in quantum affine algebras and related
              topics ({R}aleigh, {NC}, 1998)},
    SERIES = {Contemp. Math.},
    VOLUME = {248},
     PAGES = {243--291},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1999}}

@article{Lenart_2014,
    AUTHOR = {Lenart, Cristian and Naito, Satoshi and Sagaki, Daisuke and
              Schilling, Anne and Shimozono, Mark},
     TITLE = {A uniform model for {K}irillov-{R}eshetikhin crystals {I}:
              {L}ifting the parabolic quantum {B}ruhat graph},
   JOURNAL = {Int. Math. Res. Not. IMRN},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
      YEAR = {2015},
    NUMBER = {7},
     PAGES = {1848--1901}, 
       DOI = {10.1093/imrn/rnt263},
       URL = {https://doi.org/10.1093/imrn/rnt263},
}

@misc{lenart2008combinatorial,
      title={On Combinatorial Formulas for Macdonald Polynomials}, 
      author={Cristian Lenart},
      year={2008},
      eprint={0804.4716},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@article{LENARTCharge,
title = {From Macdonald polynomials to a charge statistic beyond type A},
journal = {J. Combin. Theory Ser. A},
volume = {119},
number = {3},
pages = {683-712},
year = {2012},
doi = {https://doi.org/10.1016/j.jcta.2011.11.013},
url = {https://www.sciencedirect.com/science/article/pii/S0097316511001889},
author = {Cristian Lenart},
keywords = {Macdonald polynomials, Alcove walks, Ram–Yip formula, Kashiwara–Nakashima columns, Charge statistic},
}

@article {lenart2010halllittlewood,
    AUTHOR = {Lenart, C.},
     TITLE = {Hall-{L}ittlewood polynomials, alcove walks, and fillings of
              {Y}oung diagrams},
   JOURNAL = {Discrete Math.},
    VOLUME = {311},
      YEAR = {2011},
    NUMBER = {4},
     PAGES = {258--275},
          ISSN = {0012-365X,1872-681X}}

@article{Ion,
author = {Ion, B.},
title = {{Nonsymmetric Macdonald polynomials and Demazure characters}},
volume = {116},
journal = {Duke Math. J.},
number = {2},
publisher = {Duke University Press},
pages = {299 -- 318},
year = {2003},
doi = {10.1215/S0012-7094-03-11624-5},
}