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Singularity of orbital measures in SU(n)

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Abstract

We show that the minimalk such that μκ ∈L 1(SU(n)) for all central, continuous measures μ on SU(n) isk=n. We do this by exhibiting an elementg∈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 n-1 g is singular toL 1.

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Author notes

  1. Sanjiv Kumar Gupta

    Present address: Department of Mathematics and Statistics, sultan Qaboos University, A1 Khodh 123, P.O. Box 36, Sultanate of Oman

Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, N2L 3G1, Ontario, Waterloo, Canada

    Sanjiv Kumar Gupta & Kathryn E. Hare

Authors
  1. Sanjiv Kumar Gupta
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  2. Kathryn E. Hare
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Correspondence to Sanjiv Kumar Gupta.

Additional information

This research is supported in part by NSERC. The hospitality of the University of Waterloo is gratefully acknowledged.

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Gupta, S.K., Hare, K.E. Singularity of orbital measures in SU(n). Isr. J. Math. 130, 93–107 (2002). https://doi.org/10.1007/BF02764072

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  • DOI: https://doi.org/10.1007/BF02764072

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