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

作者：Karolyi Gyula^*; Nagy Zoltan Lorant; Petrov Fedor V; Volkov Vladislav

来源：Advances in Mathematics, 2015, 277: 252-282.

DOI：10.1016/j.aim.2014.09.028

• Aomoto's constant term identity
• Calogero-Sutherland model
• Combinatorial Nullstellensatz
• Erdos-Heilbronn conjecture
• Forrester's conjecture
• Hermite interpolation
• Selberg integral

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.

• 出版日期2015-6-4