On the affine analogue of Jack and Macdonald polynomials
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Publication:1902009
DOI10.1215/S0012-7094-95-07810-7zbMATH Open0873.33011arXivhep-th/9403168MaRDI QIDQ1902009
Author name not available (Why is that?)
Publication date: 7 January 1996
Published in: (Search for Journal in Brave)
Abstract: We define the analogue of Jack's (Jacobi) polynomials, which were defined for finite-dimensional root system by Heckman and Opdam as eigenfunctions of trigonometric Sutherland operator for the affine root system . In the affine case, we define the polynomials as eigenfunctions of "affine Sutherland operator", which is Calogero-Sutherland operator with elliptic potential plus the term involving derivative with respect to the modular parameter. We show that such polynomials can be constructed explicitly as traces of certain intertwiners for affine Lie algebra. Also, we define the q-analogue of this construction, which gives affine analogues of Macdonald's polynomials, and show the (conjectured) relation between the Macdonald's inner product identities for affine case and scalar product of conformal blocks in the WZW model.
Full work available at URL: https://arxiv.org/abs/hep-th/9403168
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