The modular branching rule for affine Hecke algebras of type A

TL;DR

This paper establishes a clear correspondence between geometric and combinatorial simple modules for affine Hecke algebras of type A at roots of unity and proves a generalized modular branching rule.

Contribution

It explicitly links geometric and combinatorial models of simple modules and extends the modular branching rule beyond previous results by Vazirani.

Findings

Established the correspondence between geometric and combinatorial simple modules.

Proved the generalized modular branching rule for affine Hecke algebras of type A.

Extended Vazirani's work on modular branching rules.

Abstract

For the affine Hecke algebra of type A at roots of unity, we make explicit the correspondence between geometrically constructed simple modules and combinatorially constructed simple modules and prove the modular branching rule. The latter generalizes work by Vazirani.