On the dimension datum of a subgroup

Abstract

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.