L2-singular dichotomy for orbital measures of classical simple Lie algebras

Sanjiv Kumar Gupta, Kathryn E. Hare, Sobhan Seyfaddini

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either μk is singular to Lebesgue measure or μk ∈ L2. The minimum k for which μk ∈ L2 is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.

Original languageEnglish
Pages (from-to)91-124
Number of pages34
JournalMathematische Zeitschrift
Volume262
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Simple Lie Algebra
Dichotomy
Orbit
Simple group
Lebesgue Measure
Smoothness
Lie Algebra
Fold
Invariant

Keywords

  • Adjoint orbit
  • Classical Lie algebra
  • Compact Lie group
  • Conjugacy class
  • Orbital measure

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

L2-singular dichotomy for orbital measures of classical simple Lie algebras. / Gupta, Sanjiv Kumar; Hare, Kathryn E.; Seyfaddini, Sobhan.

In: Mathematische Zeitschrift, Vol. 262, No. 1, 2009, p. 91-124.

Research output: Contribution to journalArticle

Gupta, Sanjiv Kumar ; Hare, Kathryn E. ; Seyfaddini, Sobhan. / L2-singular dichotomy for orbital measures of classical simple Lie algebras. In: Mathematische Zeitschrift. 2009 ; Vol. 262, No. 1. pp. 91-124.
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