Hilbert series of invariants, constant terms and Kostka–Foulkes polynomials

A problem that arose in the study of the mass of the neutrino led us to the evaluation of a constant term with a variety of ramifications into several areas from Invariant Theory, Representation Theory, the Theory of Symmetric Functions and Combinatorics. A significant by-product of our evaluation is the construction of a trigraded Cohen Macaulay basis for the Invariants under an action of SLn(C)SLn(C) on a space of 2n+n22n+n2 variables.