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Affine Analogue of Jack's Polynomials for \hat{sl}_2

Yuji Hara
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Abstract

Affine analogue of Jack's polynomials introduced by Etingof and Kirillov Jr. is studied for the case of \hat{sl}_2. 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 SL_2(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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Yuji Hara. 2003-12-24. Affine Analogue of Jack's Polynomials for \hat{sl}_2. https://arxiv.org/abs/math/0210236

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