Singular characters and their L^p norms on classical Lie groups

Saverio Giulini

Vol. 109 (1983), No. 2, 387–398

DOI: 10.2140/pjm.1983.109.387

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 {λ_n} in the dual object Ĝ such that d_λn →∞ and ∥χ_λn∥_p ≤ 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