Vol. 109, No. 2, 1983

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Singular characters and their Lp norms on classical Lie groups

Saverio Giulini

Vol. 109 (1983), No. 2, 387–398
Abstract

We show that the Weyl’s characters formula takes a particular form in the case of representations whose maximal weight is singular. This formula enables us to prove the following statement. Let G be a compact connected Lie group such that the complexification of its Lie algebra is a direct sum of its center with classical Lie algebras; then there exists a sequence {λn} in the dual object Ĝ such that dλn →∞ and χλnp K(p) < for all n and for all p < 3.

Mathematical Subject Classification 2000
Primary: 22E46
Secondary: 42A55, 43A75
Milestones
Received: 25 November 1981
Revised: 5 August 1982
Published: 1 December 1983
Authors
Saverio Giulini