Rings of regular functions on nilpotent orbits and their covers
type: Item
instance of: scholarly article
title: Rings of regular functions on nilpotent orbits and their covers
zbMATH Open document ID: 0648.22004
DOI: 10.1007/BF01850661
author: William M. McGovern
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143699
review text: Let G be a complex semisimple algebraic group with Lie algebra \({\mathfrak g}\). Let \({\mathfrak O}\subset {\mathfrak g}\) be a nilpotent G-orbit, R(\({\mathfrak O})\) its ring of regular functions. We derive a formula for R(\({\mathfrak O})\) as a G-module and prove some partial results on \(R(\widetilde{\mathfrak O})\), \(\widetilde{\mathfrak O}\) a cover of \({\mathfrak O}\). We then relate this formula to various existing multiplicity formulas for K-types in Harish-Chandra bimodules of G.
reviewed by: William M. McGovern
Mathematics Subject Classification ID: 22E10
Mathematics Subject Classification ID: 22E60
Mathematics Subject Classification ID: 43A22
zbMATH DE Number: 4057828
zbMATH Keywords: complex semisimple algebraic group
zbMATH Keywords: Lie algebra
zbMATH Keywords: ring of regular functions
zbMATH Keywords: multiplicity formulas
zbMATH Keywords: Harish-Chandra bimodules
MaRDI profile type: Publication
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OpenAlex ID: W2002342100
description: scientific article; zbMATH DE number 4057828