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 μk is singular to L1. For Lie groups other than type Bn or C3 this result is sharp.
| Original language | English |
|---|---|
| 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
Singularity of orbits in classical lie algebras. / Gupta, Sanjiv Kumar; Hare, Kathryn E.
In: Geometric and Functional Analysis, Vol. 13, No. 4, 2003, p. 815-844.Research output: Contribution to journal › Article
}
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.
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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 -