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

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

2005-12-02

arxiv.org/abs/math/0512046v1

Mathematics

Representation Theory

24 pages

Scientific paper

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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