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Hermitian representations of the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$

Yun Gao·Ziting Zeng
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Abstract

We use the idea of free fields to obtain highest weight representations for the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$ coordinatized by the quantum torus $\bc_q$ and go on to construct a contravariant hermitian form. We further give a necessary and sufficient condition such that the contravariant hermitian form is positive definite.

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BibTeXRIS

Yun Gao, Ziting Zeng. 2005-12-02. Hermitian representations of the extended affine Lie algebra $\widetilde{\frak{gl}_{2}(\bc_q)}$. https://arxiv.org/abs/math/0512046

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