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Caractères virtuels de groupes de Lie compacts connexes qui divisent un caractère. (Generalized characters of compact connected Lie groups that divide characters). (French) Zbl 0606.22010

This paper proves the following theorem: Let G be a compact connected Lie group. Let \(\psi\) be a virtual character of G; (i.e. the difference of two characters of finite dimensional representations). Assume that \(\psi |_ T\), where T is a maximal torus, divides a character of T. Then for any character \(\chi\) having the same irreducible components as \(\psi\), there is an integer m such that \(\chi^ m \psi\) or \(-\chi^ m \psi\) is a character of G.
The proof depends on results of the author showing when the coefficients of a polynomial of form \(P^ n f\) are positive for some integer n [Ergodic Theory Dyn. Syst. 6, 57-79 (1986; Zbl 0606.22005)].
Reviewer: R.Fabec

MSC:

22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
43A77 Harmonic analysis on general compact groups
22C05 Compact groups

Citations:

Zbl 0606.22005
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