Geodesic
The Bailey lemma and Kostka polynomials
Journal of Algebraic Combinatorics, Tome 20 (2004) no. 2, pp. 131-171.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $^{(1)} _{ n-1}$ and to identities for A-type branching functions.
Classification : Primary, 05A19,, 05E05,, 11B65;, Secondary, 17B65,, 33D15
Keywords: Kostka polynomials, bailey's lemma, branching functions, $q$-series 
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     title = {The {Bailey} lemma and {Kostka} polynomials},
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Warnaar, S.Ole. The Bailey lemma and Kostka polynomials. Journal of Algebraic Combinatorics, Tome 20 (2004) no. 2, pp. 131-171. http://geodesic.mathdoc.fr/item/JAC_2004__20_2_a4/