Steklov Institute of Mathematics at St.Petersburg

PREPRINT 4/1996

THE q-ANALOGUE OF MODEL SPACE AND CGC GENERATING MATRICES

This preprint was accepted January 1996.
Contact: A. Bytsko and L.Faddeev

ABSTRACT:
The $q$-analogue $(T^*B)_q$ of the phase space $T^*B$ for the Borel
subgroup $B$ of a given simple Lie group $G$ is constructed and studied. It is
shown to give a $q$-analogue of the model representation for the group $G$. A
particular "coordinatization" of $(T^*B)_q$ (in the case of $G=SL(2)$) is
given in terms of matrix generating corresponding Clebsch-Gordan coefficients
(CGC).