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We give a basis of the finite dimensional irreducible representation of U q (X n ) (X=B, C, D) with highest weight NΛ 1 (N∈Z≥0), which we call «symmetric tensor representation». This basis is orthonormal and consists of weight vectors. The action of U q (X n ) is given explicitly

A basis of symmetric tensor representations for the quantum analogue of the Lie algebras {$B\sb n$}, {$C\sb n$} and