Vol. 84, No. 1, 1979

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Asymptotic behavior of multiplicities of representations of compact groups

Robert S. Cahn and Michael E. Taylor

Vol. 84 (1979), No. 1, 17–28

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 Rk, 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
Received: 1 June 1978
Published: 1 September 1979
Robert S. Cahn
Michael E. Taylor
Mathematics Dept.
Univ. of North Carolina
Chapel Hill NC 27599
United States