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 -