A generalization of the q-Saalschutz sum and the Burge transform

1999/09/08 by A. Schilling, S. O. Warnaar
Mathematics · #math.QA #math.CO #msc:33D15 #msc:05A30 #msc:05A10

paper · pdf

published as in: Physical Combinatorics, M. Kashiwara and T. Miwa (eds.), Birkhäuser Boston, Cambridge, MA, 2000, pp. 163-183. · 18 pages, AMSLaTeX

arxiv created 1999/09/08 · arxiv updated 2009/11/30

Abstract

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A₁⁽¹⁾ string functions.

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