Intersection matrix of a generalized Airy function in terms of skew-Schur polynomials

Abstract

A duality is introduced between a pair of polynomial twisted de Rham cohomology groups associated with a generalized Airy function in several variables. Natural bases of the twisted de Rham groups are constructed in terms of Schur polynomials. Then the intersection matrix relative to these bases is calculated explicitly in terms of skew-Schur polynomials.