Quantum Kac-Moody Algebras and Vertex Representations

Mathematics – Quantum Algebra

Scientific paper

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

Scientific paper

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.

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