On the affine analogue of Jack's and Macdonald's polynomials

Details On the affine analogue of Jack's and Macdonald's polynomials On the affine analogue of Jack's and Macdonald's polynomials

1994-03-28

arxiv.org/abs/hep-th/9403168v2

Physics

High Energy Physics

High Energy Physics - Theory

27 pages. Revised version; minor corrections

Scientific paper

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 $\hat A_{n-1}$. 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.

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