A new approach to constant term identities and Selberg-type integrals |
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Authors: | Gyula Ká rolyi,Zoltá n Ló rá nt Nagy,Fedor V. Petrov,Vladislav Volkov |
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Affiliation: | 1. MTA Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, 1053, Hungary;2. Steklov Institute of Mathematics, Fontanka 27, 191023 St. Petersburg, Russia;3. Saint-Petersburg State University, Universitetsky prospekt 28, 198504 St. Petersburg, Russia |
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Abstract: | Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics. |
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Keywords: | Aomoto's constant term identity Calogero&ndash Sutherland model Combinatorial Nullstellensatz Erd?s&ndash Heilbronn conjecture Forrester's conjecture Hermite interpolation Selberg integral |
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