Generalized Jack polynomials and the AGT relations for the $SU(3)$ group

Abstract

We find generalized Jack polynomials for the group $SU(3)$ and verify that their Selberg averages for several first levels are given by Nekrasov functions. To compute the averages we derive recurrence relations for the $sl_3$ Selberg integrals.

6 pages, refs added, typos corrected, published version