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String functions and cyclotomic Hecke algebras

  • Dennis Stanton
  • Ting Xue
  • Ae Ja Yee
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Abstract

In this paper we study the Kleshchev multipartitions that label simple modules of certain cyclotomic Hecke algebras with parameters $1$ and −1. The $2$-residue statistic divides these multipartitions into blocks. We deduce a bivariate generating function for the blocks using representation theory. We also relate the generating functions of multipartitions in a fixed block to string functions associated by Kac and Peterson to irreducible highest weight modules of a type A1(1) affine Lie algebra. By considering matrices formed by these generating functions, we reprove some results of Kac--Peterson on string functions using the Macdonald identities of Rosengren--Schlosser. As an application, we obtain new infinite product formulas for these generating functions.

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Cite

BibTeXRIS
BibTeX
@misc{stanton2026string,
  title = {{String functions and cyclotomic Hecke algebras}},
  author = {Dennis Stanton and Ting Xue and Ae Ja Yee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22669},
  eprint = {2610.22669},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22669},
}
RIS
TY  - UNPB
TI  - String functions and cyclotomic Hecke algebras
AU  - Dennis Stanton
AU  - Ting Xue
AU  - Ae Ja Yee
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22669
UR  - https://arxiv.org/abs/2610.22669
AB  - In this paper we study the Kleshchev multipartitions that label simple modules of certain cyclotomic Hecke algebras with parameters $1$ and −1. The $2$-residue statistic divides these multipartitions into blocks. We deduce a bivariate generating function for the blocks using representation theory. We also relate the generating functions of multipartitions in a fixed block to string functions associated by Kac and Peterson to irreducible highest weight modules of a type A_1^(1) affine Lie algebra. By considering matrices formed by these generating functions, we reprove some results of Kac--Peterson on string functions using the Macdonald identities of Rosengren--Schlosser. As an application, we obtain new infinite product formulas for these generating functions.
ER  -