Quantized flag manifolds and irreducible *-representations

Details Quantized flag manifolds and irreducible *-representations Quantized flag manifolds and irreducible *-representations

1998-02-18

arxiv.org/abs/math/9802086v1

Mathematics

Quantum Algebra

AMS-LaTeX v1.2, 27 pages, no figures

Scientific paper

10.1007/s002200050613

We study irreducible *-representations of a certain quantization of the algebra of polynomial functions on a generalized flag manifold regarded as a real manifold. All irreducible *-representations are classified for a subclass of flag manifolds containing in particular the irreducible compact Hermitian symmetric spaces. For this subclass it is shown that the irreducible *-representations are parametrized by the symplectic leaves of the underlying Poisson bracket. We also discuss the relation between the quantized flag manifolds studied in this paper and the quantum flag manifolds studied by Soibelman, Lakshimibai and Reshetikhin, Jurco and Stovicek, and Korogodsky.

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