Modular representations and branching rules for wreath Hecke algebras

TL;DR

This paper introduces wreath Hecke algebras as a generalization of degenerate affine Hecke algebras, classifies their simple modules over fields of any characteristic, and establishes modular branching rules linked to quantum affine algebra crystal graphs.

Contribution

It generalizes the concept of degenerate affine Hecke algebras to wreath Hecke algebras and classifies their simple modules over arbitrary characteristic fields.

Findings

Classified simple modules of wreath Hecke algebras.

Derived modular branching rules for these algebras.

Connected branching rules to crystal graphs of quantum affine algebras.

Abstract

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are classified over an algebraically closed field of any characteristic p. The modular branching rules for these algebras are obtained, and when p does not divide the order of G, they are further identified with crystal graphs of integrable modules for quantum affine algebras. The key is to establish an equivalence between a module category of the (cyclotomic) wreath Hecke algebra and its suitable counterpart for the degenerate affine Hecke algebra.