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

Yun Gao, Ziting Zeng

Published 2005-12-02Version 1

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.