Singularity of orbital measures in SU(n)

Sanjiv Kumar Gupta; Kathryn E. Hare

doi:10.1007/BF02764072

Singularity of orbital measures in SU(n)

Sanjiv Kumar Gupta, Kathryn E. Hare

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

7 Citations (Scopus)

Abstract

We show that the minimal k such that μ^k ∈ L¹ (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μ_g is the corresponding orbital measure supported on the conjugacy class, then μ_g^n-1 is singular to L¹.

Original language	English
Article number	BF02764072
Pages (from-to)	93-107
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	130
DOIs	https://doi.org/10.1007/BF02764072
Publication status	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02764072

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abstract = "We show that the minimal k such that μk ∈ L1 (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μg is the corresponding orbital measure supported on the conjugacy class, then μgn-1 is singular to L1.",

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AB - We show that the minimal k such that μk ∈ L1 (SU(n)) for all central, continuous measures μ on SU(n) is k = n. We do this by exhibiting an element g ∈ SU(n) for which the (n - 1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μg is the corresponding orbital measure supported on the conjugacy class, then μgn-1 is singular to L1.

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Singularity of orbital measures in SU(n)

Abstract

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