Communications in Mathematical Physics

, Volume 203, Issue 2, pp 297–324 | Cite as

Quantized Flag Manifolds and Irreducible *-Representations

  • Jasper V. Stokman
  • Mathijs S. Dijkhuizen


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 Soibel'man, Lakshimibai & Reshetikhin, Juračo & Šťovíček and Korogodsky.


Manifold Symmetric Space Polynomial Function Poisson Bracket Hermitian Symmetric Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jasper V. Stokman
    • 1
  • Mathijs S. Dijkhuizen
    • 2
  1. 1.KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The NetherlandsNL
  2. 2.Department of Mathematics, Faculty of Science, Kobe University, Rokko, Kobe 657, JapanJP

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