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arxiv: 0708.1193 · v1 · submitted 2007-08-08 · 🧮 math.CA · math.CO· math.QA

A Selberg integral for the Lie algebra A_n

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A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.

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    Proves uniqueness of solutions to constraints on (q,t)-deformed hypergeometric functions and derives superintegrability relations for a general (q,t)-deformed matrix model with allowed parameters.