Work

String functions and cyclotomic Hecke algebras

Year: 2026

Type: article

Abstract: In this paper, we study the Kleshchev multipartitions that label simple modules of certain cyclotomic Hecke algebras with parameters 1 and $$-1$$ - 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 $$A_1^{(1)}$$ 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.

Source: Research in the Mathematical Sciences

DOI: 10.1007/s40687-026-00669-0

Authors: Dennis Stanton, Ting Xue, Ae Ja Yee

Institutions: University of Minnesota, The University of Melbourne, Pennsylvania State University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,090

Funder: Australian Research Council