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

The unitary irreducible representations of the uq(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 uq(2,1) superset of uq(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