Representations of quantum algebra Uq(uₙ,₁)

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Infinite dimensional representations of the real form Uq(uₙ,₁) of the Drinfeld--Jimbo algebra Uq(glₙ₊₁) are defined. The principal series of representations of Uq(uₙ,₁) is studied. Intertwining operators for pairs of the principal series representations are calculated in an explicit form. The structure of reducible representations of the principal series is determined. Irreducible representations of Uq(uₙ,₁), obtained from irreducible and reducible principal series representations, are classified. All *-representations in this set of irreducible representations are separated. Unlike the classical case, the algebra Uq(uₙ,₁) has finite dimensional irreducible *-representations.