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(9月15日)On the structure of cyclotomic nilHecke algebras
来源: 陈黎   发布时间:2017-9-11   阅读次数:440

报告题目: On the structure of cyclotomic nilHecke algebras

报告人:胡峻 教授

摘要: In this talk we shall consider the structure of the cyclotomic nilHecke Hecke algebras $\HH_{\ell,n}^{(0)}$, where $\ell,n\in\N$. We construct a monomial basis for $\HH_{\ell,n}^{(0)}$ which verifies a conjecture of Mathas. We show that the graded basic algebra of $\HH_{\ell,n}^{(0)}$ is commutative and hence isomorphic to the center $Z$ of $\HH_{\ell,n}^{(0)}$. We further prove that $\HH_{\ell,n}^{(0)}$ is isomorphic to the full matrix algebra over $Z$ and construct an explicit basis for the center $Z$. We also construct a complete set of pairwise orthogonal primitive idempotents of $\HH_{\ell,n}^{(0)}$. Finally, we present a new homogeneous symmetrizing form $\Tr$ on $\HH_{\ell,n}^{(0)}$ by explicitly specifying its value on every graded cellular basis element of $\HH_{\ell,n}^{(0)}$ and show that it coincides with Shan--Varagnolo--Vasserot's symmetrizing form $\Tr^{\text{SVV}}$ on $\HH_{\ell,n}^{(0)}$.

 This is a joint work with Xinfeng Liang.

地点:欧阳楼314

时间:9月15日上午三四节课

联系人:李方 教授(fangli@zju.edu.cn)

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