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arXiv · 2409.09372

Markov traces on degenerate cyclotomic Hecke algebras

Deke Zhao
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Abstract

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

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BibTeXRIS

Deke Zhao. 2024-09-14. Markov traces on degenerate cyclotomic Hecke algebras. https://arxiv.org/abs/2409.09372

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