Quantum Kac-Moody Algebras and Vertex Representations

TL;DR

This paper introduces an affinization of quantum Kac-Moody algebras, constructs vertex operator representations from bosonic fields, and derives a combinatorial identity involving Hall-Littlewood polynomials, advancing the understanding of algebraic and combinatorial structures.

Contribution

It presents a novel affinization of quantum Kac-Moody algebras and constructs their vertex representations, along with a new combinatorial identity related to Hall-Littlewood polynomials.

Findings

Constructed a new affinization of quantum Kac-Moody algebra.

Developed vertex operator representations from bosonic fields.

Derived a combinatorial identity involving Hall-Littlewood polynomials.

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.