Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 1

Affine analogue of Jack's polynomials for sl2 (hat)

Pages: 87 – 120

DOI: http://dx.doi.org/10.4310/ATMP.2003.v7.n1.a4

Author

Yuji Hara

Abstract

Affine analogue of Jack's polynomials introduced by Etingof and Kirillov Jr. is studied for the case of sl2 (hat). Using the Wakimoto representation, we give an integral formula of elliptic Selberg type for the affine Jack's polynomials. From this integral formula, the action of SL2(Z) on the space of the affine Jack's polynomials is computed. For simple cases, we write down the affine Jack's polynomials in terms of some modular and elliptic functions.

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