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arXiv · 1901.00222

Deformed Poisson W-algebras of Type A

Lachlan Walker
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Abstract

For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to conjugacy classes in $SL_{l+1}(\mathbb{C})$ as a polynomial algebra of invariants. These may be viewed as an algebraic group analogue of certain graded parabolic invariants that generate the (graded) W-algebra in type A.

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Lachlan Walker. 2019-01-01. Deformed Poisson W-algebras of Type A. https://arxiv.org/abs/1901.00222

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