Isomorphisms between affine Hecke algebras

TL;DR

This paper establishes a precise criterion for when two affine Hecke algebras of type A_n are isomorphic, showing they are isomorphic if and only if their parameters are inverses or equal.

Contribution

The paper proves a complete characterization of isomorphisms between affine Hecke algebras of type A_n based on their parameters.

Findings

Affine Hecke algebras $H_q$ and $H_p$ are isomorphic iff $p=q^{ ext{±}1}$.

The result provides a clear parameter condition for algebra isomorphism.

The proof clarifies the structure of affine Hecke algebras in relation to their parameters.

Abstract

Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$.