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$SU_3$ coherent state operators and invariant correlation functions and their quantum group counterparts

H. Sazdjian·Y. S. Stanev·I. T. Todorov
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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 $SU_3$. 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 $U_q(sl_3)$ invariant 2-point functions for representaions of the type $(λ,0)$ and $(0,λ)$. General invariant 2-point functions are written down in a mixed Poincaré-Birkhoff-Witt type basis.

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H. Sazdjian, Y. S. Stanev, I. T. Todorov. 1994-09-05. $SU_3$ coherent state operators and invariant correlation functions and their quantum group counterparts. https://doi.org/10.1063/1.531100

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