Quantum Kac-Moody Algebras and Vertex Representations

Abstract

We introduce an affinization of the quantum Kac-Moody algebra associated to a symmetric generalized Cartan matrix. Based on the affinization, we construct a representation of the quantum Kac-Moody algebra by vertex operators from bosonic fields. We also obtain a combinatorial indentity about Hall-Littlewood polynomials.

12 pages Latex2e, corrected some typos, to appear in Lett. Math. Phys. Sub-ject: Quantum Algebra

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