## Abstract

We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either μ^{k} is singular to Lebesgue measure or μ^{k} ∈ L^{2}. The minimum k for which μ^{k} ∈ L^{2} is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.

Original language | English |
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Pages (from-to) | 91-124 |

Number of pages | 34 |

Journal | Mathematische Zeitschrift |

Volume | 262 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

## Keywords

- Adjoint orbit
- Classical Lie algebra
- Compact Lie group
- Conjugacy class
- Orbital measure

## ASJC Scopus subject areas

- Mathematics(all)

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