### Abstract

We prove that if μ_{a} = m_{k}*δ_{a}*m_{K} is the K-bi-invariant measure supported on the double coset K a K {succeeds or equal to} SU (n), for K = SO(n), then μ_{a}
^{k} is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μ_{a}, supported on the minimal dimension double coset has the property that μ_{a}
^{n-1} is singular to the Haar measure.

Original language | English |
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Pages (from-to) | 27-43 |

Number of pages | 17 |

Journal | Monatshefte fur Mathematik |

Volume | 159 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

### Keywords

- Absolutely continuous measure
- Bi-invariant measure
- SU(n)
- Symmetric space

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Gupta, S. K., & Hare, K. E. (2009). Smoothness of convolution powers of orbital measures on the symmetric space SU(n)/SO(n).

*Monatshefte fur Mathematik*,*159*(1), 27-43. https://doi.org/10.1007/s00605-008-0029-3