A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras $B_n$, $C_n$ and $D_n$

Toshiki Nakashima

doi:10.2977/prims/1195170856

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

A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras $B_{n}$ , $C_{n}$ and $D_{n}$

Toshiki Nakashima
Kyoto University, Japan

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Abstract

We give a basis of the finite dimensional irreducible representation of $U_{q} (X_{n})$ ( $X = B, C, D$ ) with highest weight $N Λ_{1}$ ( $N \in Z_{\geq 0}$ ), 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.

Cite this article

Toshiki Nakashima, A Basis of Symmetric Tensor Representations for the Quantum Analogue of the Lie Algebras $B_{n}$ , $C_{n}$ and $D_{n}$ . Publ. Res. Inst. Math. Sci. 26 (1990), no. 4, pp. 723–733

DOI 10.2977/PRIMS/1195170856