Open Access
January, 1999 Associated variety, Kostant-Sekiguchi correspondence, and locally free U(n)-action on Harish-Chandra modules
Akihiko GYOJA, Hiroshi YAMASHITA
J. Math. Soc. Japan 51(1): 129-149 (January, 1999). DOI: 10.2969/jmsj/05110129

Abstract

Let g be acomplex semisimple Lie algebra with symmetric decomposition g=k+p. For each irreducible Harish-Chandra (g,k)-module X, we construct a family of nilpotent Lie subalgebras n(O) of g whose universal enveloping algebras U(n(O)) act on X locally freely. The Lie subalgebras n(O) are parametrized by the nilpotent orbits O in the associated variety of X, and they are obtained by making use of the Cayley tranformation of sI2-triples(Kostant-Sekiguchi correspondence). As aconsequence, it is shown that an irreducible Harish-Chandra module has the possible maximal Gelfand-Kirillov dimension if and only if it admits locally free U(nm)-action for nm=n(Omax) attached to aprincipal nilpotent orbit Omax in p.

Citation

Download Citation

Akihiko GYOJA. Hiroshi YAMASHITA. "Associated variety, Kostant-Sekiguchi correspondence, and locally free U(n)-action on Harish-Chandra modules." J. Math. Soc. Japan 51 (1) 129 - 149, January, 1999. https://doi.org/10.2969/jmsj/05110129

Information

Published: January, 1999
First available in Project Euclid: 10 June 2008

MathSciNet: MR1661024
zbMATH: 0931.22008
Digital Object Identifier: 10.2969/jmsj/05110129

Subjects:
Primary: 22E47
Secondary: 17B35

Keywords: associated variety , Harish-Chandra modules , locally free action , Nilpotent orbits , Semisimple Lie algebras

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 1 • January, 1999
Back to Top