On Weyl modules of cyclotomic $q$-Schur algebras

TL;DR

This paper derives character formulas for Weyl modules of cyclotomic q-Schur algebras using Kostka numbers and generalized Littlewood-Richardson rules, with applications to modular representation theory.

Contribution

It provides explicit character formulas and explores symmetric functions related to Weyl modules of cyclotomic q-Schur algebras, extending previous combinatorial methods.

Findings

Character formulas expressed via Kostka numbers and generalized Littlewood-Richardson coefficients

Analysis of symmetric functions associated with Weyl modules

Applications to modular representations of cyclotomic q-Schur algebras

Abstract

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule. We also study corresponding symmetric functions. Finally, we give some simple applications to modular representations of cyclotomic $q$-Schur algebras.