SU3 coherent state operators and invariant correlation functions and their quantum group counterparts

Abstract

Coherent state operators (CSOs) are defined as operator valued functions on G=SL(n,C) being 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. CSOs provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of SU3. The quantum group deformation of the construction gives rise to a noncommutative coset space. A ‘‘standard’’ polynomial basis is introduced in this space (related to but not identical with the Lusztig canonical basis) that is appropriate for writing down Uq(sl3) invariant 2-point functions for representations of the type (λ,0) and (0,λ). General invariant 2-point functions are written down in a mixed Poincaré–Birkhoff–Witt type basis.