### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis

### Cite this

*Geometric and Functional Analysis*,

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

**Singularity of orbits in classical lie algebras.** / Gupta, Sanjiv Kumar; Hare, Kathryn E.

Research output: Contribution to journal › Article

*Geometric and Functional Analysis*, vol. 13, no. 4, pp. 815-844. https://doi.org/10.1007/s00039-003-0431-x

}

TY - JOUR

T1 - Singularity of orbits in classical lie algebras

AU - Gupta, Sanjiv Kumar

AU - Hare, Kathryn E.

PY - 2003

Y1 - 2003

N2 - 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 μk is singular to L1. For Lie groups other than type Bn or C3 this result is sharp.

AB - 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 μk is singular to L1. For Lie groups other than type Bn or C3 this result is sharp.

UR - http://www.scopus.com/inward/record.url?scp=0141764882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141764882&partnerID=8YFLogxK

U2 - 10.1007/s00039-003-0431-x

DO - 10.1007/s00039-003-0431-x

M3 - Article

VL - 13

SP - 815

EP - 844

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 4

ER -