On representation theory of affine Hecke algebras of type B

TL;DR

This paper extends the representation theory framework of affine Hecke algebras from type A to type B with unequal parameters, achieving classification and multiplicity results under specific eigenvalue restrictions.

Contribution

It adapts Ariki's and Grojnowski's methods to type B affine Hecke algebras with unequal parameters, providing new classification and multiplicity-one results.

Findings

Established multiplicity-one results for type B

Classified irreducible representations under certain eigenvalue conditions

Derived partial branching rules similar to type A

Abstract

Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators -- analogous multiplicity-one results and a classification of irreducibles with partial branching rules as in type $A$.