Proceedings of the International Conference on Geometry, Integrability and Quantization

Quantization Operators and Invariants of Group Representations

Andrés Viña

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.

Article information

Source
Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2012), 265-277

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815531

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

Mathematical Reviews number (MathSciNet)
MR3087977

Zentralblatt MATH identifier
1382.53026

Citation

Viña, Andrés. Quantization Operators and Invariants of Group Representations. Proceedings of the Thirteenth International Conference on Geometry, Integrability and Quantization, 265--277, Avangard Prima, Sofia, Bulgaria, 2012. doi:10.7546/giq-13-2012-265-277. https://projecteuclid.org/euclid.pgiq/1436815531


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