JournalsprimsVol. 26, No. 4pp. 723–733

A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras <i>B<sub>n</sub></i>, <i>C<sub>n</sub></i> and <i>D<sub>n</sub></i>

  • Toshiki Nakashima

    Kyoto University, Japan
A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras <i>B<sub>n</sub></i>, <i>C<sub>n</sub></i> and <i>D<sub>n</sub></i> cover
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Abstract

We give a basis of the finite dimensional irreducible representation of Uq(Xn) (X=B,C,D) with highest weight _N⋀_1 (_N_∈ ℤ ≥ 0), which we call "symmetric tensor representation". This basis is orthonormal and consists of weight vectors. The action of Uq(Xn) is given explicitly.

Cite this article

Toshiki Nakashima, A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras <i>B<sub>n</sub></i>, <i>C<sub>n</sub></i> and <i>D<sub>n</sub></i>. Publ. Res. Inst. Math. Sci. 26 (1990), no. 4, pp. 723–733

DOI 10.2977/PRIMS/1195170856