2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76583We 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 AlgebraQuantum Algebratext