$S{U}_3$ coherent state operators and invariant correlation functions and their quantum group counterparts

Abstract

Coherent state operators (CSO) are defined as operator valued functions on G=SL(n,C), homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSO provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of $S{U}_3$. The quantum group deformation of the construction gives rise to a non-commutative coset space. We introduce a "standard" polynomial basis in this space (related to but not identical with the Lusztig canonical basis) which is appropriate for writing down $U_q(s{l}_3)$ invariant 2-point functions for representaions of the type $(\lambda ,0)$ and $(0,\lambda )$. General invariant 2-point functions are written down in a mixed Poincaré-Birkhoff-Witt type basis.

33 pages, LATEX, preprint IPNO/TH 94-01

References in corpus (2)

• su(3)k fusion coefficients
• Bicovariant differential geometry of the quantum group GL_q(3)

Cited by in corpus (6)

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• Representations of $U_h(su(N))$ derived from quantum flag manifolds
• Categorified symmetries
• Self-adjoint extension for Maxwell-Chern-Simons model in long wavelength limit
• Localizations for construction of quantum coset spaces
• A construction of representations and quantum homogeneous spaces