Duke Math. J. 165 (14), 2683-2736, (1 October 2016) DOI: 10.1215/00127094-3619898
KEYWORDS: dimension datum, Sato–Tate measure, root system, automorphism group, Weyl group, weight, character, generating function, 22E55, 58J53
The dimension datum of a closed subgroup of a compact Lie group is the sequence of invariant dimensions of irreducible representations by restriction. In this article we classify connected closed subgroups of a given compact Lie group with equal dimension data or linearly dependent dimension data. We also study the equalities and linear relations among dimension data of closed subgroups of a unitary group which act irreducibly on the natural representation.