L2-singular dichotomy for orbital measures of classical simple Lie algebras

被引：13
作者：
Gupta, Sanjiv Kumar [2 ]
Hare, Kathryn E. [1 ]
Seyfaddini, Sobhan [3 ]
机构：
[1] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada
[2] Sultan Qaboos Univ, Dept Math & Stat, Al Khoud 123, Oman
[3] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
MATHEMATISCHE ZEITSCHRIFT | 2009年 / 262卷 / 01期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Classical Lie algebra; Compact Lie group; Adjoint orbit; Conjugacy class; Orbital measure; HARMONIC-ANALYSIS; SINGULAR-INTEGRALS; NILPOTENT GROUPS; CHARACTERS; NORMS; SIZE;
D O I：
10.1007/s00209-008-0364-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the G-invariant orbital measures supported on adjoint orbits in the Lie algebra of a classical, compact, connected, simple Lie group satisfy a smoothness dichotomy: Either mu(k) is singular to Lebesgue measure or mu(k) is an element of L-2. The minimum k for which mu(k) is an element of L-2 is specified and is also the minimum k such that the k-fold sum of the orbit has positive measure.
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页码：91 / 124
页数：34
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