TY - JOUR

T1 - Singularity of orbits in classical lie algebras

AU - Gupta, Sanjiv Kumar

AU - Hare, Kathryn E.

N1 - Funding Information:
This research was supported in part by NSERC, the Swedish natural sciences research council and the Sultan Qaboos University, Oman. The hospitality of the Department of Mathematics of Goteborg University and Chalmers Inst. of Tech., where both authors visited, and the Department of Pure Mathematics at the University of Waterloo where the first author visited, is gratefully appreciated.

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.

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U2 - 10.1007/s00039-003-0431-x

DO - 10.1007/s00039-003-0431-x

M3 - Article

AN - SCOPUS:0141764882

VL - 13

SP - 815

EP - 844

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

SN - 1016-443X

IS - 4

ER -