Singularity of orbits in classical lie algebras

Sanjiv Kumar Gupta; Kathryn E. Hare

doi:10.1007/s00039-003-0431-x

Singularity of orbits in classical lie algebras

Sanjiv Kumar Gupta, Kathryn E. Hare

Mathematics & Statistics

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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 μ^k is singular to L¹. For Lie groups other than type B_n or C₃ this result is sharp.

Original language	English
Pages (from-to)	815-844
Number of pages	30
Journal	Geometric and Functional Analysis
Volume	13
Issue number	4
DOIs	https://doi.org/10.1007/s00039-003-0431-x
Publication status	Published - 2003

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ASJC Scopus subject areas

Mathematics(all)
Analysis

Cite this

Gupta, S. K., & Hare, K. E. (2003). Singularity of orbits in classical lie algebras. Geometric and Functional Analysis, 13(4), 815-844. https://doi.org/10.1007/s00039-003-0431-x

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10.1007/s00039-003-0431-x