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- W4225550237 abstract "For any positive integer $n$, let $A_n=mathbb{C}[t_1,dots,t_n]$, $W_n=text{Der}(A_n)$ and $Delta_n=text{Span}{frac{partial}{partial{t_1}},dots,frac{partial}{partial{t_n}}}$. Then $(W_n, Delta_n)$ is a Whittaker pair. A $W_n$-module $M$ on which $Delta_n$ operates locally finite is called a Whittaker module. We show that each block $Omega_{mathbf{a}}^{widetilde{W}}$ of the category of $(A_n,W_n)$-Whittaker modules with finite dimensional Whittaker vector spaces is equivalent to the category of finite dimensional modules over $L_n$, where $L_n$ is the Lie subalgebra of $W_n$ consisting of vector fields vanishing at the origin. As a corollary, we classify all simple non-singular Whittaker $W_n$-modules with finite dimensional Whittaker vector spaces using $mathfrak{gl}_n$-modules. We also obtain an analogue of Skryabin's equivalence for the non-singular block $Omega_{mathbf{a}}^W$." @default.
- W4225550237 created "2022-05-05" @default.
- W4225550237 creator A5022504253 @default.
- W4225550237 creator A5083718637 @default.
- W4225550237 date "2021-12-27" @default.
- W4225550237 modified "2023-09-29" @default.
- W4225550237 title "Whittaker category for the Lie algebra of polynomial vector fields" @default.
- W4225550237 hasPublicationYear "2021" @default.
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