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Published December 2021 | public
Journal Article Open

AFLT-type Selberg integrals


In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for a Selberg integral over the product of two Jack polynomials, thereby unifying the well-known Kadell and Hua–Kadell integrals. In this paper we use a variety of symmetric functions and symmetric function techniques to prove generalisations of the AFLT integral. These include (i) an A_n analogue of the AFLT integral, containing two Jack polynomials in the integrand; (ii) a generalisation of (i) for γ = 1 (the Schur or GUE case), containing a product of n+1 Schur functions; (iii) an elliptic generalisation of the AFLT integral in which the role of the Jack polynomials is played by a pair of elliptic interpolation functions; (iv) an AFLT integral for Macdonald polynomials.

Additional Information

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. Received: 5 February 2020; Accepted: 27 June 2021. Work supported by the Australian Research Council Discovery Grant DP170102648.

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Accepted Version - 2001.05637.pdf


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August 20, 2023
August 20, 2023