The L2-singular dichotomy for exceptional lie groups and algebras

K. E. Hare, D. L. Johnstone, F. Shi, W. K. Yeung

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

We show that every orbital measure, μx, on a compact exceptional Lie group or algebra has the property that for every positive integer either μxK ∈ L2 and the support of μxK has non-empty interior, or μ xK is singular to Haar measure and the support of μxK has Haar measure zero. We also determine the index k where the change occurs; it depends on properties of the set of annihilating roots of x. This result was previously established for the classical Lie groups and algebras. To prove this dichotomy result we combinatorially characterize the subroot systems that are kernels of certain homomorphisms.

Original languageEnglish (US)
Pages (from-to)362-382
Number of pages21
JournalJournal of the Australian Mathematical Society
Volume95
Issue number3
DOIs
StatePublished - Dec 1 2013

Keywords

  • Adjoint orbit
  • Conjugacy class
  • Exceptional Lie group/algebra
  • Orbital measure
  • Root system

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