The dichotomy problem for orbital measures of SU(n)

Sanjiv Gupta; Kathryn E. Hare

doi:10.1007/s00605-005-0321-4

The dichotomy problem for orbital measures of SU(n)

Sanjiv Gupta^*, Kathryn E. Hare

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

For many orbital measures μ, on SU(n), we show that either μ^k L ² or μ^k is singular to L ¹. The least k for which μ^k L ² is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital measures satisfy this dichotomy.

Original language	English
Pages (from-to)	227-238
Number of pages	12
Journal	Monatshefte fur Mathematik
Volume	146
Issue number	3
DOIs	https://doi.org/10.1007/s00605-005-0321-4
Publication status	Published - Nov 2005

Keywords

Compact Lie group
Orbital measure
Tangent space

ASJC Scopus subject areas

General Mathematics

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10.1007/s00605-005-0321-4

Cite this

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abstract = "For many orbital measures μ, on SU(n), we show that either μk L 2 or μk is singular to L 1. The least k for which μk L 2 is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital measures satisfy this dichotomy.",

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AB - For many orbital measures μ, on SU(n), we show that either μk L 2 or μk is singular to L 1. The least k for which μk L 2 is determined and is shown to be the minimum k for which the k-fold product of the conjugacy class supporting the measure has positive measure. It would be interesting to know if all orbital measures satisfy this dichotomy.

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KW - Orbital measure

KW - Tangent space

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The dichotomy problem for orbital measures of SU(n)

Abstract

Keywords

ASJC Scopus subject areas

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