Markov traces on degenerate cyclotomic Hecke algebras

Abstract

Let $H_n(\mathbf{u})$ be the degenerate cyclotomic Hecke algebra with parameter $\mathbf{u}=(u_1,\dots ,u_m)$ over $\mathbb{C}(\mathbf{u})$. We define and construct the (non-)normalized Markov traces on the sequence $\{H_n(\mathbf{u}){\}}_{n=1}^{\infty }$. This allows us to provide a canonical symmetrizing form on $H_n(\mathbf{u})$ and show that the Brudan--Kleshchev trace on $H_n(\mathbf{u})$ is a specialization of the non-normalized Markov traces.

We made several improvements to the paper in response to referee comments