Open Access
2011 Quantization Operators and Invariants of Group Representations
Andrés Viña
J. Geom. Symmetry Phys. 24: 89-102 (2011). DOI: 10.7546/jgsp-24-2011-89-102


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 ${\rm Ham}(M)$, the Hamiltonian group of $M$. We also interpret geometrically the values of the infinitesimal character of $\pi$ in terms of quantization operators.


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Andrés Viña. "Quantization Operators and Invariants of Group Representations." J. Geom. Symmetry Phys. 24 89 - 102, 2011.


Published: 2011
First available in Project Euclid: 25 May 2017

zbMATH: 1248.53076
MathSciNet: MR2932788
Digital Object Identifier: 10.7546/jgsp-24-2011-89-102

Rights: Copyright © 2011 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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