The sl_3 Selberg integral

Details The sl_3 Selberg integral The sl_3 Selberg integral

2009-01-27

arxiv.org/abs/0901.4176v3

Advances in Mathematics 224 (2010) 499-524

Mathematics

Classical Analysis and ODEs

23 pages

Scientific paper

10.1016/j.aim.2009.11.011

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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