9 research outputs found
Quantized flag manifolds and irreducible *-representations
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.Comment: AMS-LaTeX v1.2, 27 pages, no figure
CQG algebras: a direct algebraic approach to compact quantum groups
The purely algebraic notion of CQG algebra (algebra of functions on a compact
quantum group) is defined. In a straightforward algebraic manner, the
Peter-Weyl theorem for CQG algebras and the existence of a unique positive
definite Haar functional on any CQG algebra are established. It is shown that a
CQG algebra can be naturally completed to a -algebra. The relations
between our approach and several other approaches to compact quantum groups are
discussed.Comment: 14 pp., Plain TeX, accepted by Lett. Math. Phy