@misc{shimozonocrysdum,
    author = "M.~Shimozono",
    title = "Crystals for Dummies",
    year = 2005,
    howpublished = "\url{https://www.aimath.org/WWN/kostka/crysdumb.pdf}"
}

@article {chmutovlewispylyavskyy23,
    AUTHOR = {M.~Chmutov and J.~Lewis and P.~Pylyavskyy},
     TITLE = {Monodromy in {K}azhdan-{L}usztig cells in affine type {A}},
   JOURNAL = {Math. Ann.},
    VOLUME = {386},
      YEAR = {2023},
    NUMBER = {3-4},
     PAGES = {1891--1949},
       DOI = {10.1007/s00208-022-02434-4},
}

@article {schutzenberger72,
    AUTHOR = {M.~P.~Sch\"utzenberger},
     TITLE = {Promotion des morphismes d'ensembles ordonn\'es},
   JOURNAL = {Discrete Math.},
    VOLUME = {2},
      YEAR = {1972},
     PAGES = {73--94},
}

@article {shimozono02,
  AUTHOR = {M.~Shimozono},
  TITLE = {Affine type {A} crystal structure on tensor products of rectangles, {D}emazure characters, and nilpotent varieties},
  JOURNAL = {J. Algebraic Combin.},
  VOLUME = {15},
  YEAR = {2002},
  NUMBER = {2},
  PAGES = {151--187},
  DOI = {10.1023/A:1013894920862},
}
@book {fulton97,
    AUTHOR = {W.~Fulton},
     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},
}

@article{assaf08crystals,
    title      = {A combinatorial realization of {S}chur-{W}eyl duality via crystal graphs and dual equivalence graphs},
    author     = {Assaf, S.},
    doi        = {10.46298/dmtcs.3626},
    journal    = {Discrete Math. Theor. Comput. Sci. Proc.},
    volume     = {AJ},
    PAGES = {141--152},
    year       = {2008},
    language   = {English},
}

@article {assaf15,
    AUTHOR = {S.~Assaf},
     TITLE = {Dual equivalence graphs {I}: {A} new paradigm for {S}chur
              positivity},
   JOURNAL = {Forum Math. Sigma},
  FJOURNAL = {Forum of Mathematics. Sigma},
    VOLUME = {3},
      YEAR = {2015},
     PAGES = {Paper No. e12, 33 pp.},
      ISSN = {2050-5094},
       DOI = {10.1017/fms.2015.15},
       URL = {https://doi.org/10.1017/fms.2015.15},
}

@article {shi91,
    AUTHOR = {J.~Y.~Shi},
     TITLE = {The generalized {R}obinson-{S}chensted algorithm on the affine
              {W}eyl group of type {$\tilde A_{n-1}$}},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {139},
      YEAR = {1991},
    NUMBER = {2},
     PAGES = {364--394},
       DOI = {10.1016/0021-8693(91)90300-W},
       URL = {https://doi.org/10.1016/0021-8693(91)90300-W},
}
@article {chmutovpylyavskyyyudovina18,
    AUTHOR = {M.~Chmutov and P.~Pylyavskyy and E.~Yudovina},
     TITLE = {Matrix-ball construction of affine {R}obinson-{S}chensted
              correspondence},
   JOURNAL = {Selecta Math. (N.S.)},
  FJOURNAL = {Selecta Mathematica. New Series},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {2},
     PAGES = {667--750},
       DOI = {10.1007/s00029-018-0402-6},
}

@article {chmutov15,
    AUTHOR = {M.~Chmutov},
     TITLE = {Type {$A$} molecules are {K}azhdan-{L}usztig},
   JOURNAL = {J. Algebraic Combin.},
  FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal},
    VOLUME = {42},
      YEAR = {2015},
    NUMBER = {4},
     PAGES = {1059--1076},
       DOI = {10.1007/s10801-015-0616-z},
       URL = {https://doi.org/10.1007/s10801-015-0616-z},
}

@article {assafbilley12,
    AUTHOR = {S.~Assaf and S.~Billey},
     TITLE = {Affine dual equivalence and {$k$}-{S}chur functions},
   JOURNAL = {J. Comb.},
  FJOURNAL = {Journal of Combinatorics},
    VOLUME = {3},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {343--399},
       DOI = {10.4310/JOC.2012.v3.n3.a5},
       URL = {https://doi.org/10.4310/JOC.2012.v3.n3.a5},
}

@book{bumpschilling17,
  title={Crystal Bases: Representations And Combinatorics},
  author={Bump, D. and Schilling, A.},
  isbn={9789814733465},
  year={2017},
  publisher={World Scientific Publishing Company}
}


@article {DLT94,
    AUTHOR = {J.~D\'esarm\'enien and B.~Leclerc and J.~Y.~Thibon},
     TITLE = {Hall-{L}ittlewood functions and {K}ostka-{F}oulkes polynomials
              in representation theory},
   JOURNAL = {S\'em. Lothar. Combin.},
  FJOURNAL = {S\'eminaire Lotharingien de Combinatoire},
    VOLUME = {32},
      YEAR = {1994},
     PAGES = {Art. B32c, approx. 38},
   MRCLASS = {05E05 (20G05)},
  MRNUMBER = {1399504},
}
@incollection {Foulkes72,
    AUTHOR = {H.~O.~Foulkes},
     TITLE = {Characters of symmetric groups induced by characters of cyclic
              subgroups},
 BOOKTITLE = {Combinatorics ({P}roc. {C}onf. {C}ombinatorial {M}ath.,
              {M}ath. {I}nst., {O}xford, 1972)},
     PAGES = {141--154},
 PUBLISHER = {Inst. Math. Appl., Southend-on-Sea},
      YEAR = {1972},
}

@book{stanley_fomin_1999, place={Cambridge}, series={Cambridge Studies in Advanced Mathematics}, title={Enumerative Combinatorics}, volume={2},  publisher={Cambridge University Press}, author={R.~P.~Stanley}, year={1999}, collection={Cambridge Studies in Advanced Mathematics}}

@article{kang92,
title = {Affine crystals and vertex models},
author = {S.~J.~Kang and M.~Kashiwara and K.~C.~Misra and T.~Miwa and T.~Nakashima and A.~Nakayashiki},
journal = {Int. J. Mod. Phys. A},
number = {1},
pages = {449--484},
volume = {7},
year = {1992},
DOI = {10.1142/s0217751x92003896},
}

@article{Kashiwara1991,
  title={On crystal bases of the {$Q$}-analogue of universal enveloping algebras},
  author={M.~Kashiwara},
  journal={Duke Math. J.},
  year={1991},
  volume={63},
  pages={465-516},
}

@article{KR1990,
  title={Representations of {Y}angians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras},
  author={A.~N.~Kirillov and N.~Reshetikhin},
  journal={J. Sov. Math.},
  year={1990},
  volume={52},
  pages={3156-3164},
}

@article{Stembridge08,
author = {J.~R.~Stembridge},
year = {2008},
month = {10},
pages = {346-368},
title = {Admissible ${W}$-graphs},
volume = {12},
journal = {Represent. Theory},
doi = {10.1090/S1088-4165-08-00336-1}
}

@article{Stembridge12,
title = {A finiteness theorem for ${W}$-graphs},
journal = {Adv. Math.},
volume = {229},
number = {4},
pages = {2405-2414},
year = {2012},
doi = {https://doi.org/10.1016/j.aim.2012.01.008},
author = {J.~R.~Stembridge},
keywords = {Kazhdan–Lusztig basis, -graph, Cell, Strongly regular graph},
}

@article{lenarttravis19,
title = {On higher level {K}irillov–{R}eshetikhin crystals, {D}emazure crystals, and related uniform models},
journal = {J. Algebra},
volume = {539},
pages = {285-304},
year = {2019},
doi = {https://doi.org/10.1016/j.jalgebra.2019.07.036},
author = {C.~Lenart and T.~Scrimshaw},
keywords = {Kirillov–Reshetikhin crystal, Demazure crystal, Quantum alcove model},
}

@article{naoi13,
title = {{D}emazure crystals and tensor products of perfect {K}irillov–{R}eshetikhin crystals with various levels},
journal = {J. Algebra},
volume = {374},
pages = {1-26},
year = {2013},
issn = {0021-8693},
doi = {https://doi.org/10.1016/j.jalgebra.2012.10.020},
url = {https://www.sciencedirect.com/science/article/pii/S0021869312005315},
author = {K.~Naoi},
keywords = {Kirillov–Reshetikhin crystal, Demazure crystal, Energy function},
}

@article{schillingtingley11,
author = {A.~Schilling and P.~Tingley},
year = {2011},
month = {04},
pages = {},
title = {{D}emazure Crystals, {K}rillov-{R}eshetikhin Crystals, and the Energy Function},
volume = {19},
journal = {Electron. J. Combin.},
doi = {10.37236/2184}
}

@article{lnsss14,
    author = {C.~Lenart and S.~Naito and D.~Sagaki and A.~Schilling and M.~Shimozono},
    title = {A Uniform Model for {K}irillov–{R}eshetikhin Crystals {I}: Lifting the Parabolic Quantum {B}ruhat Graph},
    journal = {Int. Math. Res. Not.},
    volume = {2015},
    number = {7},
    pages = {1848-1901},
    year = {2014},
    month = {01},
}

@article{lnsss16,
    author = {C.~Lenart and S.~Naito and D.~Sagaki and A.~Schilling and M.~Shimozono},
    title = {A Uniform Model for {K}irillov–{R}eshetikhin Crystals {II}. Alcove Model, Path Model, and {P}$=${X}},
    journal = {Int. Math. Res. Not.},
    volume = {2017},
    number = {14},
    pages = {4259-4319},
    year = {2016},
    month = {07},
    issn = {1073-7928},
    doi = {10.1093/imrn/rnw129},
    eprint = {https://academic.oup.com/imrn/article-pdf/2017/14/4259/18767656/rnw129.pdf},
}


@article{lnsss17,
	author = {C.~Lenart and S.~Naito and D.~Sagaki and A.~Schilling and M.~Shimozono},
	da = {2017/12/01},
	date-added = {2025-09-28 14:32:30 -0500},
	date-modified = {2025-09-28 14:32:30 -0500},
	doi = {10.1007/s00031-017-9421-1},
	id = {LENART2017},
	isbn = {1531-586X},
	journal = {Transform. Groups},
	number = {4},
	pages = {1041--1079},
	title = {A UNIFORM MODEL FOR {K}IRILLOV--{R}ESHETIKHIN CRYSTALS {III}: NONSYMMETRIC {M}ACDONALD POLYNOMIALS AT $t = 0$ AND {D}EMAZURE CHARACTERS},
	ty = {JOUR},
	url = {https://doi.org/10.1007/s00031-017-9421-1},
	volume = {22},
	year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00031-017-9421-1}}

@article {kraskiewiczweyman01,
    AUTHOR = {W.~Kra\'skiewicz and J.~Weyman},
     TITLE = {Algebra of coinvariants and the action of a {C}oxeter element},
   JOURNAL = {Bayreuth. Math. Schr.},
  FJOURNAL = {Bayreuther Mathematische Schriften},
    VOLUME = {63},
      YEAR = {2001},
     PAGES = {265--284},
      ISSN = {0172-1062},
   MRCLASS = {20C30 (05E10 17B01)},
  MRNUMBER = {1867283},
MRREVIEWER = {Christine\ Bessenrodt},
}
@article {LLT94,
    AUTHOR = {A.~Lascoux and B.~Leclerc and J.Y.~Thibon},
     TITLE = {Green polynomials and {H}all-{L}ittlewood functions at roots
              of unity},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {15},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {173--180},
       DOI = {10.1006/eujc.1994.1019},
}
@misc{brauneretal25,
      title={Crystal skeletons: Combinatorics and axioms}, 
      author={S.~Brauner and S.~Corteel and Z.~Daugherty and A.~Schilling},
      eprint={2503.14782},
      eprinttype={arxiv},
      year={2025},
      archivePrefix={arXiv},
      primaryClass={math.CO},
}

@article{LS1978,
  author    = {A.~Lascoux and M.~Sch{\"u}tzenberger},
  title     = {Sur une conjecture de {H}. {O}. {F}oulkes},
  journal   = {C. R. Acad. Sci. Paris Sér. A-B},
  volume    = {286},
  year      = {1978},
  pages     = {A323--A324}
}

@incollection{LS1984,
  author    = {A.~Lascoux and M.~Sch{\"u}tzenberger},
  title     = {Tableaux and the {L}ittlewood--{R}ichardson Rule},
  booktitle = {Combinatorics and Algebra},
  series    = {Contemp. Math.},
  volume    = {34},
  pages     = {161--190},
  publisher = {Amer. Math. Soc.},
  year      = {1984}
}

@article{NY1997,
  author    = {A.~Nakayashiki and Y.~Yamada},
  title     = {Kostka polynomials and energy functions in solvable lattice models},
  journal   = {Selecta Math.},
  volume    = {3},
  number    = {4},
  pages     = {547--599},
  year      = {1997},
  doi       = {10.1007/s000290050013}
}

@article{Shimozono1995,
  author    = {M.~Shimozono},
  title     = {A cyclage poset structure for {L}ittlewood--{R}ichardson tableaux},
  journal   = {European J. Combin.},
  volume    = {16},
  number    = {5},
  pages     = {447--462},
  year      = {1995},
  doi       = {10.1016/0195-6698(95)90002-0}
}

@article {loehrwarrington12,
    AUTHOR = {N.~Loehr and G.~Warrington},
     TITLE = {Quasisymmetric expansions of {S}chur-function plethysms},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {140},
      YEAR = {2012},
    NUMBER = {4},
     PAGES = {1159--1171},
      ISSN = {0002-9939,1088-6826},
}

@article {Iijima13,
    AUTHOR = {K.~Iijima},
     TITLE = {A {$q$}-multinomial expansion of {LLT} coefficients and
              plethysm multiplicities},
   JOURNAL = {European J. Combin.},
    VOLUME = {34},
      YEAR = {2013},
    NUMBER = {6},
     PAGES = {968--986},
       DOI = {10.1016/j.ejc.2013.01.007},
}

@article{mgt22,
      title={Splitting the square of homogeneous and elementary functions into their symmetric and anti-symmetric parts}, 
      author={F.~Maas-Gariépy and E.~Tétreault},
      year={2022},
      journal={arXiv:2203.08279},
      eprint={2203.08279},
      archivePrefix={arXiv},
      primaryClass={math.CO},
}

@article{carre1995,
  title={Splitting the square of a {S}chur function into its symmetric and antisymmetric parts},
  author={C.~Carr{\'e} and B.~Leclerc},
  journal={J. Algebraic Combin.},
  volume={4},
  number={3},
  pages={201--231},
  year={1995},
  publisher={Springer}
}
@misc{mpw2025krdeg,
      title={{K}irillov--{R}eshetikhin dual equivalence graphs}, 
      author={McDonough, J. and Pylyavskyy, P. and Wang, S.},
      year={2025},
      eprint={2510.24490},
      archivePrefix={arxiv},
      primaryClass={math.CO},
}
@article {akasakakashiwara97,
    AUTHOR = {Akasaka, T. and Kashiwara, M.},
     TITLE = {Finite-dimensional representations of quantum affine algebras},
   JOURNAL = {Publ. Res. Inst. Math. Sci.},
  FJOURNAL = {Kyoto University. Research Institute for Mathematical
              Sciences. Publications},
    VOLUME = {33},
      YEAR = {1997},
    NUMBER = {5},
     PAGES = {839--867},
       DOI = {10.2977/prims/1195145020},
}