The Bailey lemma and Kostka polynomials

Abstract

Using 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-LaTeX

References in corpus (2)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Conjugate Bailey pairs