Involutions of Iwahori-Hecke algebras and representations of fixed subalgebras

TL;DR

This paper explores the structure and representation theory of fixed subalgebras of Iwahori-Hecke algebras of types B and D, establishing branching rules and classifying irreducible representations using Clifford theory.

Contribution

It introduces new branching rules for fixed subalgebras of Iwahori-Hecke algebras and determines their irreducible representations, expanding understanding of their algebraic structure.

Findings

Established branching rules between type B and D Iwahori-Hecke algebras and their fixed subalgebras.

Determined basic sets of irreducible representations for these fixed subalgebras.

Applied generalized Clifford theory to classify irreducible representations.

Abstract

We establish branching rules between some Iwahori-Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The Iwahori-Hecke algebra of type D is one of such fixed subalgebras. We also obtain branching rules between those fixed subalgebras and their intersection subalgebra. We determine basic sets of irreducible representations of those fixed subalgebras and their intersection subalgebra by making use of generalized Clifford theory.