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arXiv · 1710.05514

Centers and Azumaya loci of finite $W$-algebras

Bin Shu·Yang Zeng
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Abstract

In this paper, we study the center $Z$ of the finite $W$-algebra $\mathcal{T}(\mathfrak{g},e)$ associated with a semi-simple Lie algebra $\mathfrak{g}$ over an algebraically closed field $\mathds{k}$ of characteristic $p\gg0$, and an arbitrarily given nilpotent element $e\in\mathfrak{g}$. We obtain an analogue of Veldkamp's theorem on the center. For the maximal spectrum $\text{Specm}(Z)$, we show that its Azumaya locus coincides with its smooth locus of smooth points. The former locus reflects irreducible representations of maximal dimension for $\mathcal{T}(\mathfrak{g},e)$.

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BibTeXRIS

Bin Shu, Yang Zeng. 2017-10-16. Centers and Azumaya loci of finite $W$-algebras. https://doi.org/10.1017/s0305004121000414

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