TY - JOUR

T1 - A new approach to constant term identities and Selberg-type integrals

AU - Károlyi, G.

AU - Nagy, Z.L.

AU - Petrov, F.V.

AU - Volkov, V.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Aomoto's constant term identity

KW - Calogero–Sutherland model

KW - Combinatorial Nullstellensatz

KW - Erdős–Heilbronn conjecture

KW - Forrester's conjecture

KW - Hermite interpolation

KW - Selberg integral

U2 - 10.1016/j.aim.2014.09.028

DO - 10.1016/j.aim.2014.09.028

M3 - Article

VL - 277

SP - 252

EP - 282

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -