The irreducible characters of the alternating Hecke algebras

TL;DR

This paper calculates the irreducible characters of alternating Hecke algebras, providing explicit character values and establishing a splitting field in the semisimple case, advancing understanding of these algebraic structures.

Contribution

It explicitly computes irreducible characters of alternating Hecke algebras and identifies a splitting field, offering new insights into their representation theory.

Findings

Character values determined on minimal length conjugacy class representatives

Irreducible characters uniquely determined by these values

Identification of a splitting field in the semisimple case

Abstract

This paper computes the irreducible characters of the alternating Hecke algebras, which are deformations of the group algebras of the alternating groups. More precisely, we compute the values of the irreducible characters of the semisimple alternating Hecke algebras on a set of elements indexed by minimal length conjugacy class representatives and we show that these character values determine the irreducible characters completely. As an application we determine a splitting field for the alternating Hecke algebras in the semisimple case.