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Highest Weight Modules over Quantum Queer Superalgebra U Q (q(n))

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra Uq(q(n)). The key ingredients are the triangular decomposition of Uq(q(n)) and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for Uq(q(n))-modules in the category O≥0 q .