The centers of Iwahori-Hecke algebras are filtered

TL;DR

This paper demonstrates that the center of the Iwahori-Hecke algebra for symmetric groups has a natural filtered algebra structure, with structure constants of the graded algebra being independent of n, and discusses related conjectures and open problems.

Contribution

It introduces a natural filtered algebra structure on the center of the Iwahori-Hecke algebra and shows the independence of structure constants from n.

Findings

Center of Iwahori-Hecke algebra has a natural filtered algebra structure

Structure constants of the graded algebra are independent of n

Includes conjectures and open problems related to the structure

Abstract

We show that the center of the Iwahori--Hecke algebra of the symmetric group $S_n$ carries a natural filtered algebra structure, and that the structure constants of the associated graded algebra are independent of $n$. A series of conjectures and open problems are also included.