A new approach to constant term identities and Selberg-type integrals
2015; Elsevier BV; Volume: 277; Linguagem: Inglês
10.1016/j.aim.2014.09.028
ISSN1090-2082
AutoresGyula Károlyi, Zoltán Lóránt Nagy, Fedor Petrov, В.В. Волков,
Tópico(s)Graph theory and applications
ResumoSelberg-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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