Aomoto's machine and the Dyson constant term identity (Q1293923)

A constant term identity allows to compute the constant term in the Laurent expansions of a function \(f(t_1,t_2, \dots,t_n)\). The main result in this paper is a constant term identity which generalizes Dyson's constant term identity [\textit{I. J. Good}, J. Math. Phys. 11, 1884 (1970)]. The proof uses as a machine Aomoto's argument, which is that the constant term in \(t_s {\partial f\over \partial t_s}(t_1,t_2, \dots,t_n)\) is zero. The author also states two conjectures: the first one generalizes the main result, and the second one is a \(q\)-analogue of the first one.