The sl_3 Selberg integral

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.

23 pages

References in corpus (4)

• A Selberg integral for the Lie algebra A_n
• Unitarity of SL(2)-conformal blocks in genus zero
• A Selberg Integral Type Formula for an sl_2 One-Dimensional Space of Conformal Blocks
• On a Selberg-Schur integral

Cited by in corpus (11)

• Matrix model version of AGT conjecture and generalized Selberg integrals
• Selberg Integral and SU(N) AGT Conjecture
• The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks
• Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
• The ${\mathbb{F}}_p$-Selberg integral of type $A_n$
• Trinion Conformal Blocks from Topological strings
• AFLT-type Selberg integrals
• Singular vectors for the $W_N$ algebras
• Heine's method and $A_n$ to $A_m$ transformation formulas
• $q$-Selberg Integrals and Koornwinder Polynomials
• Double Gegenbauer expansion of $|s-t{|}^{\alpha }$