Singularity of orbits in classical lie algebras

Sanjiv Kumar Gupta, Kathryn E. Hare

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We determine the maximum k such that the k-fold sum of some non- trivial, adjoint orbit in the Lie algebra of a classical, compact Lie group has measure zero. The orbits of minimal dimension are seen to be the extreme examples. We show that for this choice of k there is a central, continuous measure μ on the group such that μk is singular to L1. For Lie groups other than type Bn or C3 this result is sharp.

Original languageEnglish
Pages (from-to)815-844
Number of pages30
JournalGeometric and Functional Analysis
Volume13
Issue number4
DOIs
Publication statusPublished - 2003

Fingerprint

Lie Algebra
Orbit
Singularity
Compact Lie Group
Trivial
Extremes
Fold
Zero

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis

Cite this

Singularity of orbits in classical lie algebras. / Gupta, Sanjiv Kumar; Hare, Kathryn E.

In: Geometric and Functional Analysis, Vol. 13, No. 4, 2003, p. 815-844.

Research output: Contribution to journalArticle

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