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VOL. 13 | 2012 Quantization Operators and Invariants of Group Representations
Andrés Viña

Editor(s) Ivaïlo M. Mladenov, Andrei Ludu, Akira Yoshioka

Abstract

Let $G$ be a semi-simple Lie group and $\pi$ some representation of $G$ belonging to the discrete series. We give interpretations of the constant $\pi (g)$, for $g \in Z(G)$, in terms of geometric concepts associated with the flag manifold $M$ of $G$. In particular, when $G$ is compact this constant is related to the action integral around closed curves in $M$. As a consequence, we obtain a lower bound for de cardinal of the fundamental group of Ham$(M)$, the Hamiltonian group of $M$. We also interpret geometrically the values of the infinitesimal character of $\pi$ in terms of quantization operators.

Information

Published: 1 January 2012
First available in Project Euclid: 13 July 2015

zbMATH: 1382.53026
MathSciNet: MR3087977

Digital Object Identifier: 10.7546/giq-13-2012-265-277