学术报告

A Class of $\sl_{d+1}$-Modules from Witt Algebra Modules

阅读次数:1517

题目:A Class of $\sl_{d+1}$-Modules from Witt Algebra Modules
报告人:郭向前 教授 (郑州大学)
地点:致远楼108室
时间:2019年6月26日(周三) 9:00-10:00
摘要:Let $d\ge1$ be an integer, $W_d$ be the Witt  algebra. 
For any admissible $W_d$-module $P$ and any $\gl_d$-module $V$, one can form a $\W_d$-module $F(P,V)$, which as a vector space is $P\ot V$.  Since $W_d$ has a natural subalgebra isomorphic to $\sl_{d+1}$, we can view $F(P,V)$ as an $\sl_{d+1}$-module. Taking $P=\Omega(\bf{\lambda})$, the rank-$1$ $U(\mathfrak{h})$-free $W_d$-module and $V=V(\bf{a},b)$, the irreducible cuspidal module over $\gl_d$, we get the special $\sl_{d+1}$-module $\F(\bf{\lambda};\bf{a},b)=F(\Omega(\bf{\lambda}),V(\bf{a},b))$. We determine the necessary and sufficient conditions for the $\sl_{d+1}$-module $F(\bf{\lambda};\bf{a},b)$ to be irreducible. And for the reducible case, we constructed their proper submodules explicitly.

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