Sums of Adjoint Orbits

Details Sums of Adjoint Orbits Sums of Adjoint Orbits

2009-10-09

arxiv.org/abs/0910.1856v3

Advances in Mathematics 227 (2011) 253-266

Mathematics

Group Theory

16 Pages

Scientific paper

Let G be a real compact connected simple Lie group, and g its Lie algebra. We study the problem of determining, from root data, when a sum of adjoint orbits in g, or a product of conjugacy classes in G, contains an open set. Our general methods allow us to determine exactly which sums of adjoint orbits in su(m) and products of conjugacy classes in SU(m) contain an open set, in terms of the highest multiplicities of eigenvalues. For su(m) and SU(m) we show L^2--singular dichotomy: The convolution of invariant measures on adjoint orbits, or conjugacy classes, is either singular to Haar measure or in L^2.

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