Markov traces on degenerate cyclotomic Hecke algebras

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