### Abstract

We determine the maximum k such that the k-fold sum of some non- trivial, adjoint orbit in the Lie algebra of a classical, compact Lie group has measure zero. The orbits of minimal dimension are seen to be the extreme examples. We show that for this choice of k there is a central, continuous measure μ on the group such that μ^{k} is singular to L^{1}. For Lie groups other than type B_{n} or C_{3} this result is sharp.

Original language | English |
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Pages (from-to) | 815-844 |

Number of pages | 30 |

Journal | Geometric and Functional Analysis |

Volume | 13 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 |

### ASJC Scopus subject areas

- Mathematics(all)
- Analysis

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## Cite this

Gupta, S. K., & Hare, K. E. (2003). Singularity of orbits in classical lie algebras.

*Geometric and Functional Analysis*,*13*(4), 815-844. https://doi.org/10.1007/s00039-003-0431-x