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AFLT-type Selberg integrals

Albion, Seamus P. and Rains, Eric M. and Warnaar, S. Ole (2021) AFLT-type Selberg integrals. Communications in Mathematical Physics, 388 (2). pp. 735-791. ISSN 0010-3616. doi:10.1007/s00220-021-04157-0.

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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.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Albion, Seamus P.0000-0002-8930-3109
Warnaar, S. Ole0000-0002-9786-0175
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.
Funding AgencyGrant Number
Australian Research CouncilDP170102648
Issue or Number:2
Record Number:CaltechAUTHORS:20211110-164135228
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Official Citation:Albion, S.P., Rains, E.M. & Warnaar, S.O. AFLT-type Selberg integrals. Commun. Math. Phys. 388, 735–791 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111823
Deposited By: Tony Diaz
Deposited On:11 Nov 2021 19:01
Last Modified:11 Nov 2021 19:01

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