Commutative quotients of finite W-algebras

Alexander Premet

doi:10.1016/j.aim.2010.02.020

Commutative quotients of finite W-algebras

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we reduce the problem of 1-dimensional representations for the finite W-algebras and Humphreys' conjecture on small representations of reduced enveloping algebras to the case of rigid nilpotent elements in exceptional Lie algebras. We use Katsylo's results on sections of sheets to determine the Krull dimension of the largest commutative quotient of the finite W-algebra U(g,e). © 2010 Elsevier Inc.

Original language	English
Pages (from-to)	269-306
Number of pages	37
Journal	Advances in Mathematics
Volume	225
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2010.02.020
Publication status	Published - Sept 2010

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10.1016/j.aim.2010.02.020

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AB - In this paper we reduce the problem of 1-dimensional representations for the finite W-algebras and Humphreys' conjecture on small representations of reduced enveloping algebras to the case of rigid nilpotent elements in exceptional Lie algebras. We use Katsylo's results on sections of sheets to determine the Krull dimension of the largest commutative quotient of the finite W-algebra U(g,e). © 2010 Elsevier Inc.

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Commutative quotients of finite W-algebras

Abstract

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