Singularity of orbital measures in SU(n) |
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| Authors: | Sanjiv Kumar Gupta Kathryn E. Hare |
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| Affiliation: | (1) Department of Pure Mathematics, University of Waterloo, N2L 3G1 Ontario, Waterloo, Canada;(2) Present address: Department of Mathematics and Statistics, sultan Qaboos University, A1 Khodh 123, P.O. Box 36, Sultanate of Oman |
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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 g n-1 is singular toL 1. This research is supported in part by NSERC. The hospitality of the University of Waterloo is gratefully acknowledged. |
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