Asymptotic behavior of multiplicities of representations of compact groups

Robert S. Cahn and Michael E. Taylor

Vol. 84 (1979), No. 1, 17–28

DOI: 10.2140/pjm.1979.84.17

Abstract

Let G be a compact Lie group, K a compact subgroup. We denote by {λ} a complete set of irreducible unitary representations of G, which we identify with lattice points within a Weyl chamber 𝒞 in R^k, the cotangent space to a maximal torus in G. Similarly we denote by {ρ} a complete set of irreducible representations of K. The purpose of this paper is to study the asymptotic behavior of the multiplicity ν(ρ,λ) with which ρ is contained in λ, for fixed ρ, as λ →∞ in 𝒞.

Mathematical Subject Classification 2000

Primary: 22E46

Secondary: 22C05, 10J25

Milestones

Received: 1 June 1978

Published: 1 September 1979