2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164379Using the theory of Kostka polynomials, we prove an A_{n-1} version of Bailey's lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A_{n-1}^{(1)} and to identities for A-type branching functions.39 pages, AMS-LaTeXCombinatoricsQuantum AlgebraPrimary 05A19, 05E05, 11B65; Secondary 17B65, 33D15text