A Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Term Identities

Symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture and Selberg-type integrals

It is well-known that the famous Selberg integral is equivalent to the Morris constant term identity. In 1998, Baker and Forrester conjectured a generalization of the $q$-Morris constant term identity. This conjecture was proved and extended by Károlyi, Nagy, Petrov and Volkov in 2015. In this paper, we obtain two symmetric function generalizations of the $q$-Baker--Forrester ex-conjecture. These includes: (i) a $q$-Baker--Forrester type constant term identity for a product of a complete symmetric function and a Macdonald polynomial; (ii) a complete symmetric function generalization of KNPV's …

A Laurent series proof of the Habsieger-Kadell $q$-Morris Identity

We give a Laurent series proof of the Habsieger-Kadell $q$-Morris identity, which is a common generalization of the $q$-Morris identity and the Aomoto constant term identity. The proof allows us to extend the theorem for some additional parameter cases.

多分量$q$-Baker–Forrester猜想的一个证明

A proof of the multi-component $q$-Baker--Forrester conjecture

本文证明了1998年由Baker与Forrester提出的$(p+1)$分量$q$-Baker–Forrester猜想，解决了这一悬置26年的数学猜想，该猜想是$q$-Morris恒等式的多分量推广，可推导出Selberg积分的推广形式。

$q$-Baker--Forrester ex-猜想的AFLT型推广

An AFLT-type generalization of the $q$-Baker--Forrester ex-conjecture

本文利用Gessel--Xin方法和具有规定对称性的Macdonald多项式，统一了$q$-Baker--Forrester ex-猜想与AFLT型$q$-Morris恒等式这两个重要推广。

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

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 t…