Singularity of orbits in classical lie algebras

Sanjiv Kumar Gupta; Kathryn E. Hare

doi:10.1007/s00039-003-0431-x

Singularity of orbits in classical lie algebras

Sanjiv Kumar Gupta^*, Kathryn E. Hare

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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 L¹. For Lie groups other than type B_n 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	https://doi.org/10.1007/s00039-003-0431-x
Publication status	Published - 2003

ASJC Scopus subject areas

Mathematics(all)
Analysis

Access to Document

10.1007/s00039-003-0431-x

Fingerprint Dive into the research topics of 'Singularity of orbits in classical lie algebras'. Together they form a unique fingerprint.

Cite this

@article{1ddb82b87a28492982b93b9291499a9e,

title = "Singularity of orbits in classical lie algebras",

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.",

author = "Gupta, {Sanjiv Kumar} and Hare, {Kathryn E.}",

year = "2003",

doi = "10.1007/s00039-003-0431-x",

language = "English",

volume = "13",

pages = "815--844",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

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

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 -