U q(2,1) noncompact quantum algebra: Intermediate discrete series of unitary irreducible representations

Abstract

The unitary irreducible representations of the u q(2,1) quantum algebra that belong to the intermediate discrete series are considered. The q analog of the Mickelsson-Zhelobenko algebra is developed. Use is made of the U basis corresponding to the reduction u q(2,1) ⊃ u q(2). Explicit formulas for the matrix elements of the generators are obtained in this basis. The projection operator that projects an arbitrary vector onto the extremal vector of the intermediate-series representation is found.