@article {prasad-2016,
    AUTHOR = {Prasad, Dipendra},
     TITLE = {A character relationship on {${\rm GL}_n(\mathbb{C})$}},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {211},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {257--270},
   MRCLASS = {20G05 (20G20)},
  MRNUMBER = {3474964},
MRREVIEWER = {Ross Ian Lawther},
       DOI = {10.1007/s11856-015-1273-6},
}

@Book{macdonald-2015,
    AUTHOR = {Macdonald, I. G.},
     TITLE = {Symmetric functions and {H}all polynomials},
    SERIES = {Oxford Classic Texts in the Physical Sciences},
   EDITION = {Second},
      NOTE = {With contribution by A. V. Zelevinsky and a foreword by
              Richard Stanley,
              Reprint of the 2008 paperback edition [MR1354144]},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {2015},
     PAGES = {xii+475},
   MRCLASS = {05E05 (01A75 05-02 20C30 20C33 20K01 33C80 33D80)},
  MRNUMBER = {3443860},
       URL = {https://global.oup.com/academic/product/symmetric-functions-and-hall-polynomials-9780198739128?cc=in&lang=en&}
}

@article {garvan-kim-stanton-1990,
    AUTHOR = {Garvan, Frank and Kim, Dongsu and Stanton, Dennis},
     TITLE = {Cranks and {$t$}-cores},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {101},
      YEAR = {1990},
    NUMBER = {1},
     PAGES = {1--17},
   MRCLASS = {11P83 (05A17 20C30 33D80)},
  MRNUMBER = {1055707},
MRREVIEWER = {George E. Andrews},
       DOI = {10.1007/BF01231493},
}


@Book{berndt-1991,
    AUTHOR = {Berndt, Bruce C.},
     TITLE = {Ramanujan's notebooks. {P}art {III}},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1991},
     PAGES = {xiv + 510},
   MRCLASS = {01A75 (11F11 33E05)},
  MRNUMBER = {1117903},
MRREVIEWER = {R. A. Askey},
       DOI = {10.1007/978-1-4612-0965-2},
}



@article {ayyer-behrend-2019,
    AUTHOR = {Ayyer, Arvind and Behrend, Roger E.},
     TITLE = {Factorization theorems for classical group characters, with
              applications to alternating sign matrices and plane
              partitions},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {165},
      YEAR = {2019},
     PAGES = {78--105},
   MRCLASS = {20C15 (05E05 15B35)},
  MRNUMBER = {3906649},
MRREVIEWER = {M. R. Pournaki},
       DOI = {10.1016/j.jcta.2019.01.001},
}


@article {ayyer-fischer-2020,
    AUTHOR = {Ayyer, Arvind and Fischer, Ilse},
     TITLE = {Bijective proofs of skew {S}chur polynomial factorizations},
   JOURNAL = {J. Combin. Theory Ser. A},
  FJOURNAL = {Journal of Combinatorial Theory. Series A},
    VOLUME = {174},
      YEAR = {2020},
     PAGES = {105241, 40},
   MRCLASS = {05E05 (05E10 20C15)},
  MRNUMBER = {4080032},
MRREVIEWER = {Domenico Senato},
       DOI = {10.1016/j.jcta.2020.105241},
}

@INCOLLECTION{CiuKra09,
AUTHOR = {Ciucu, M. and Krattenthaler, C.},
TITLE = {A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings},
BOOKTITLE = {Advances in combinatorial mathematics},
PAGES = {39--59},
PUBLISHER = {Springer, Berlin},
YEAR = {2009},
MRNUMBER = {2683226 (2012b:05283)},
DOI = {10.1007/978-3-642-03562-3_3},
ARXIV = {0812.1251},
}

@article{AyyBehFis16,
    AUTHOR = {Ayyer, Arvind and Behrend, Roger E. and Fischer, Ilse},
     TITLE = {Extreme diagonally and antidiagonally symmetric alternating
              sign matrices of odd order},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {367},
      YEAR = {2020},
     PAGES = {107125, 56},
   MRCLASS = {05B20 (05A15 05A19 15B35 82B20 82B23)},
  MRNUMBER = {4081430},
MRREVIEWER = {M. R. Pournaki},
       DOI = {10.1016/j.aim.2020.107125},
}


@article {kostant-1976,
    AUTHOR = {Kostant, Bertram},
     TITLE = {On {M}acdonald's {$\eta $}-function formula, the {L}aplacian
              and generalized exponents},
   JOURNAL = {Advances in Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {20},
      YEAR = {1976},
    NUMBER = {2},
     PAGES = {179--212},
   MRCLASS = {10A20 (22E45)},
  MRNUMBER = {485661},
MRREVIEWER = {S. I. Gel\cprime fand},
       DOI = {10.1016/0001-8708(76)90186-9},
}

@BOOK{FulHar91,
AUTHOR = {Fulton, W. and Harris, J.},
TITLE = {Representation theory},
SERIES = {Graduate Texts in Mathematics},
VOLUME = {129},
NOTE = {A first course},
PUBLISHER = {Springer-Verlag, New York},
YEAR = {1991},
PAGES = {xvi+551},
MRNUMBER = {1153249},
DOI = {10.1007/978-1-4612-0979-9},
}


@article{rhoades-2010,
title = {Cyclic sieving, promotion, and representation theory},
journal = {Journal of Combinatorial Theory, Series A},
volume = {117},
number = {1},
pages = {38-76},
year = {2010},
doi = {https://doi.org/10.1016/j.jcta.2009.03.017},
author = {Brendon Rhoades},
keywords = {Tableau, Kazhdan–Lusztig cellular representation, Jeu-de-taquin},
abstract = {We prove a collection of conjectures of White [D. White, personal communication, 2007], as well as some related conjectures of Abuzzahab, Korson, Li, and Meyer [O. Abuzzahab, M. Korson, M. Li, S. Meyer, Cyclic and dihedral sieving for plane partitions, U. Minnesota REU Report, 2005] and of Reiner and White [V. Reiner, personal communication, 2007; D. White, personal communication, 2007], regarding the cyclic sieving phenomenon of Reiner, Stanton and White [V. Reiner, D. Stanton, D. White, The cyclic sieving phenomenon, J. Combin. Theory Ser. A 108 (2004)] as it applies to jeu-de-taquin promotion on rectangular tableaux. To do this, we use Kazhdan–Lusztig theory and a characterization of the dual canonical basis of C[x11,…,xnn] due to Skandera [M. Skandera, On the dual canonical and Kazhdan–Lusztig bases and 3412, 4231-avoiding permutations, 2006, submitted for publication]. Afterwards, we extend our results to analyzing the fixed points of a dihedral action on rectangular tableaux generated by promotion and evacuation, suggesting a possible sieving phenomenon for dihedral groups. Finally, we give applications of this theory to cyclic sieving phenomena involving reduced words for the long elements of hyperoctohedral groups and noncrossing partitions.}
}

@misc{ayyer-2021,
      title={Factorization of classical characters twisted by roots of unity}, 
      author={Arvind Ayyer and Nishu Kumari},
      year={2021},
      eprint={2109.11310},
      archivePrefix={arXiv},
      primaryClass={math.CO}
}

@book{James-Kerber-2009,
        Author = {James, Gordon~Douglas and Kerber, Adalbert},
        Lccn = {81012681},
        Publisher = {Cambridge University Press},
        Series = {Encyclopedia of Mathematics and its Applications},
        Title = {The Representation Theory of the Symmetric Group},
        Url = {https://www.cambridge.org/core/books/representation-theory-of-the-symmetric-group/F0A56D6A57B500A0884BF599234E1BF2},
        Volume = {16},
        Year = {2009},
}


@article {kratt-1999,
    AUTHOR = {Krattenthaler, C.},
     TITLE = {Advanced determinant calculus},
      NOTE = {The Andrews Festschrift (Maratea, 1998)},
   JOURNAL = {S\'{e}m. Lothar. Combin.},
  FJOURNAL = {S\'{e}minaire Lotharingien de Combinatoire},
    VOLUME = {42},
      YEAR = {1999},
     PAGES = {Art. B42q, 67},
   MRCLASS = {05A19 (15A15 33C99)},
  MRNUMBER = {1701596},
MRREVIEWER = {George E. Andrews},
       DOI = {10.1007/978-3-642-56513-7_17}
}

@article {kratt-2005,
    AUTHOR = {Krattenthaler, C.},
     TITLE = {Advanced determinant calculus: a complement},
   JOURNAL = {Linear Algebra Appl.},
  FJOURNAL = {Linear Algebra and its Applications},
    VOLUME = {411},
      YEAR = {2005},
     PAGES = {68--166},
   MRCLASS = {05A19 (05A15 15A15)},
  MRNUMBER = {2178686},
MRREVIEWER = {George E. Andrews},
       DOI = {10.1016/j.laa.2005.06.042},
}