Wreath Hecke algebras and centralizer construction for wreath products

TL;DR

This paper generalizes the centralizer construction for wreath products, connecting it to a generalized degenerate affine Hecke algebra, extending previous work on symmetric groups.

Contribution

It introduces a new structure for the centralizer of wreath products and links it to a generalized degenerate affine Hecke algebra, broadening the theoretical framework.

Findings

Established the structure of the centralizer $\

Connected the centralizer to a generalized degenerate affine Hecke algebra.

Abstract

Generalizing the centralizer construction of Molev and Olshanski on symmetric groups, we study the structures of the centralizer $\mZ_{m,n}$ of the wreath product $G_{n-m}$ in the group algebra of $G_n$ for any $n\geq m$. We establish the connection between $\mZ_{m,n}$ and a generalization of degenerate affine Hecke algebras introduced in our earlier work.