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arXiv · 0901.4176

The sl_3 Selberg integral

S. Ole Warnaar
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Abstract

Using an extension of the well-known evaluation symmetry, a new Cauchy-type identity for Macdonald polynomials is proved. After taking the classical limit this yields a new sl_3 generalisation of the famous Selberg integral. Closely related results obtained in this paper are an sl_3-analogue of the Askey-Habsieger-Kadell q-Selberg integral and an extension of the q-Selberg integral to a transformation between q-integrals of different dimensions.

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S. Ole Warnaar. 2010-06-17. The sl_3 Selberg integral. https://doi.org/10.1016/j.aim.2009.11.011

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