变性环状赫克布拉上的马尔可夫迹线

Deke Zhao
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引用次数: 0

摘要

让 $H_n(\boldsymbol{u})$ 是参数为 $\boldsymbol{u}=(u_1, \ldots, u_m)$ over $\mathbb{C}(\boldsymbol{u})$ 的退化循环赫克代数。我们定义并构建了序列 $\{H_n(\boldsymbol{u})\}_{n=1}^{infty}$ 上的(非)归一化马尔科夫迹线。这使得我们可以在 $H_n(\boldsymbol{u})$ 上提供一个典型的对称形式,并证明 $H_n(\boldsymbol{u})$ 上的布鲁丹-克莱舍夫踪迹是非归一化马尔科夫踪迹的特殊化。
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Markov traces on degenerate cyclotomic Hecke algebras
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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