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

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

1999-09-08

arxiv.org/abs/math/9909044v1

in: Physical Combinatorics, M. Kashiwara and T. Miwa (eds.), Birkh\"auser Boston, Cambridge, MA, 2000, pp. 163-183.

Mathematics

Quantum Algebra

18 pages, AMSLaTeX

Scientific paper

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 A_1^{(1)} string functions.

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