On the centre of the cyclotomic Hecke algebras of $G(m,1,2)$

TL;DR

This paper computes the center of cyclotomic Hecke algebras for the group G(m,1,2) and explores its relation to the affine Hecke algebra's center, providing insights into their structural connections.

Contribution

It explicitly determines the center of the cyclotomic Hecke algebra for G(m,1,2) and relates it to the affine Hecke algebra's center when q ≠ 1.

Findings

Center equals the image of the affine Hecke algebra's center for q ≠ 1

Provides partial discussion on the relation between centers of cyclotomic and affine Hecke algebras

Advances understanding of algebraic structures in representation theory

Abstract

We compute the centre of the cyclotomic Hecke algebra attached to $G(m,1,2)$ and show that if $q \neq 1$ it is equal to the image of the centre of the affine Hecke algebra $\Ha$. We also briefly discuss what is known about the relation between the centre of an arbitrary cyclotomic Hecke algebra and the centre of the affine Hecke algebra of type $A$.