### Abstract

We show that the minimal k such that μ^{k} ∈ L^{1} (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 L^{1}.

Original language | English |
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Pages (from-to) | 93-107 |

Number of pages | 15 |

Journal | Israel Journal of Mathematics |

Volume | 130 |

Publication status | Published - 2002 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gupta, S. K., & Hare, K. E. (2002). Singularity of orbital measures in SU(n).

*Israel Journal of Mathematics*,*130*, 93-107.