@misc{DemCrystal,
      title={Demazure crystals and the Schur positivity of Catalan functions}, 
      author={Jonah Blasiak and Jennifer Morse and Anna Pun},
      year={2020},
      eprint={2007.04952},
      archivePrefix={arXiv},
      primaryClass={math.CO},
      url={https://arxiv.org/abs/2007.04952}, 
}



@article{BMP2020,
title = {k-{S}chur expansions of {C}atalan functions},
journal = {Advances in Mathematics},
volume = {371},
pages = {107209},
year = {2020},
doi = {https://doi.org/10.1016/j.aim.2020.107209},
author = {Jonah Blasiak and Jennifer Morse and Anna Pun and Daniel Summers},
keywords = {Macdonald polynomials, Gromov-Witten invariants, Schubert structure constants, Parabolic Hall-Littlewood polynomials, Strong tableaux},
abstract = {We make a broad conjecture about the k-Schur positivity of Catalan functions, symmetric functions which generalize the (parabolic) Hall-Littlewood polynomials. We resolve the conjecture with positive combinatorial formulas in cases which address the k-Schur expansion of (1) Hall-Littlewood polynomials, proving the q=0 case of the strengthened Macdonald positivity conjecture from [24]; (2) the product of a Schur function and a k-Schur function when the indexing partitions concatenate to a partition, describing a class of Gromov-Witten invariants for the quantum cohomology of complete flag varieties; (3) k-split polynomials, solving a substantial special case of a problem of Broer and Shimozono-Weyman on parabolic Hall-Littlewood polynomials [37]. In addition, we prove the conjecture that the k-Schur functions defined via k-split polynomials [25] agree with those defined in terms of strong tableaux [21].}
}
}

@article {SW,
AUTHOR = {Mark Shimozono and Jerzy Weyman},
TITLE = {Graded characters of modules supported in the
closure of a nilpotent conjugacy class},
Journal = {Europ. J. Combinatorics},
Fjournal = {European Journal of Combinatorics},
volume = {21},
number = {2},
year = {2000},
pages = {pp 257 -- 288},
doi = {https://doi.org/10.1006/eujc.1999.0344},
} 





@article {BMPS,
AUTHOR = {Jonah Blasiak, Jennifer Morse, Anna Pun, and Daniel Summers},
TITLE = {{C}atalan functions and k-{S}chur positivity},
}

@article {Blasiak,
AUTHOR = {Jonah Blasiak},
TITLE = {An insertion algorithm for catabolizability},
Journal = {European J. Combin.},
Fjournal = {European Journal of Combinatorics},
volume = {33},
number = {2},
year = {2012},
pages = {pp. 267 -- 276},
doi = {https://doi.org/10.1016/j.ejc.2011.09.042},
}



. 
@inproceedings {Lascoux,
    AUTHOR = {Lascoux, Alain},
     TITLE = {Cyclic permutations on words, tableaux and harmonic
              polynomials},
 BOOKTITLE = {Proceedings of the {H}yderabad {C}onference on {A}lgebraic
              {G}roups ({H}yderabad, 1989)},
     PAGES = {323--347},
 PUBLISHER = {Manoj Prakashan, Madras},
      YEAR = {1991}, 
}

@article{CC,
    AUTHOR = {Carlsson, Erik and Chou, Raymond},
     TITLE = {A descent basis for the {G}arsia-{P}rocesi module},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {457},
      YEAR = {2024},
     PAGES = {Paper No. 109945, 31 pp.}, 
       DOI = {10.1016/j.aim.2024.109945},
       URL = {https://doi.org/10.1016/j.aim.2024.109945},
}

@article {LS,
AUTHOR = {Alain Lascoux and Marcel-Paul Sch\"{u}tzenberger},
TITLE = {Le mon\"{o}ıde plaxique},
Journal = {Noncommutative Structures in Algebra and Geometric Combinatorics  (Naples, 1978), Quaderni della
Ricerca Scientifica, CNR, Roma,},
volume = {109},
year = {1981},
pages = {pp 129 -- 156}
}

@article {LS1,
    AUTHOR = {Lascoux, Alain and Sch\"utzenberger, Marcel-Paul},
     TITLE = {Sur une conjecture de {H}. {O}. {F}oulkes},
   JOURNAL = {C. R. Acad. Sci. Paris S\'er. A-B},
  FJOURNAL = {Comptes Rendus Hebdomadaires des S\'eances de l'Acad\'emie des
              Sciences. S\'eries A et B},
    VOLUME = {286},
      YEAR = {1978},
    NUMBER = {7},
     PAGES = {A323--A324}, 
}
. 

@article {GP,
    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}, 
       DOI = {10.1016/0001-8708(92)90034-I},
}





@book{EC2, 
    AUTHOR = {Stanley, Richard P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
      NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey
              Fomin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581 pp.},
       DOI = {10.1017/CBO9780511609589},
       URL = {https://doi.org/10.1017/CBO9780511609589},
}


@article{deCon-Proc, 
    AUTHOR = {De Concini, Corrado and Procesi, Claudio},
     TITLE = {Symmetric functions, conjugacy classes and the flag variety},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {64},
      YEAR = {1981},
    NUMBER = {2},
     PAGES = {203--219}, 
       DOI = {10.1007/BF01389168},
       URL = {https://doi.org/10.1007/BF01389168},
}

@article{Tanisaki,
     author = {Tanisaki, Toshiyuki},
     title = {Defining ideals of the closures of the conjugacy classes and representations of the Weyl groups},
     journal = {Tohoku Math. J. (2)},
     volume = {34},
     number = {4},
     year = {1982},
     pages = { 575--585},
     language = {en},
       DOI = {10.2748/tmj/1178229158},
}

@book{Fulton-Harris,
    AUTHOR = {Fulton, William and Harris, Joe},
     TITLE = {Representation theory. A first course},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {129},
      NOTE = {
              Readings in Mathematics},
 PUBLISHER = {Springer-Verlag, NY},
      YEAR = {1991},
     PAGES = {xvi+551 pp.}, 
       DOI = {10.1007/978-1-4612-0979-9},
       URL = {https://doi.org/10.1007/978-1-4612-0979-9},
}

@article{Springer1978, title = { A construction of representations of {W}eyl groups}, author = {Tonny Albert Springer},
year = {1978}, 
journal = { Inventiones mathematicae},
Volume = {44},
pages = {279-293},
doi = {10.1007/BF01403165}
}

@article{Springer1976,
author = {Tonny Albert Springer},
journal = {Inventiones mathematicae},
pages = {173-208},
title = {Trigonometric Sums, Green Functions on Finite Groups and Representation of Weyl Groups.},
url = {http://eudml.org/doc/142418},
volume = {36},
year = {1976},
}


@article{garsia-stanton,
title = {Group actions on {S}tanley-{R}eisner rings and invariants of permutation groups},
journal = {Advances in Mathematics},
volume = {51},
number = {2},
pages = {107-201},
year = {1984},
doi = {https://doi.org/10.1016/0001-8708(84)90005-7},
author = {Adriano M. Garsia and Dennis Stanton},
abstract = {Let H be a group of permutations of x1 ,…, xn and let QH[x1 , x2 ,…, xn] denote the ring of H-invariant Polynomials in x1 , x2 ,…, xn with rational coefficients. Combinatorial methods for the explicit construction of free bases for QH[x1 , x2 ,…, xn] as a module over the symmetric polynomials are developed. The methods are developed by studying the action of the symmetric group on the Stanley-Reisner ring of the subset lattice. Some general results are also obtained by studying the action of a Coxeter group on the Stanley-Reisner ring of the corresponding Coxeter complex. In the case of a Weyl group, a purely combinatorial construction of certain invariants first considered by R. Steinberg (Topology14 (1975), 173–177) is obtained. Some applications to representation theory are also included.}
}

@article{HottaSpringer,
    AUTHOR = {Hotta, R. and Springer, T. A.},
     TITLE = {A specialization theorem for certain {W}eyl group
              representations and an application to the {G}reen polynomials
              of unitary groups},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {41},
      YEAR = {1977},
    NUMBER = {2},
     PAGES = {113--127}, 
       DOI = {10.1007/BF01418371},
       URL = {https://doi.org/10.1007/BF01418371},
}

@book{macdonald,
    AUTHOR = {Macdonald, I. G.},
     TITLE = {Symmetric functions and {H}all polynomials},
    SERIES = {Oxford Mathematical Monographs},
   EDITION = {Second},
      NOTE = {With contributions by A. Zelevinsky,
              Oxford Science Publications},
 PUBLISHER = {The Clarendon Press, Oxford University Press, New York},
      YEAR = {1995},
     PAGES = {x+475 pp.},
}


@book{butler,
  title={Subgroup Lattices and Symmetric Functions},
  author={Butler, L.M.},
  lccn={lc94026457},
  series={American Mathematical Society: Memoirs of the American Mathematical Society},
  url={https://books.google.com/books?id=EY3UCQAAQBAJ},
  year={1994},
  publisher={American Mathematical Society}
}
a

@misc{hanada,
      title={A charge monomial basis of the Garsia-Procesi ring}, 
      author={Mitsuki Hanada},
      year={2024},
      eprint={2410.15514},
      archivePrefix={arXiv},
      primaryClass={math.CO}, 
}

@article{HHL,
    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},
       URL = {https://doi.org/10.1090/S0894-0347-05-00485-6},
}