Stokes matrices of hypergeometric integrals (Q968263)

The authors compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. The hypergeometric integrals contain an exponential term \(e^{-\lambda f_0}\), where \(f_0\) is an extra linear form. Differentiating with respect to \(\lambda\), one obtains a differential equation satisfied by these integrals. (Such equations appear in the analysis of a probabilistic model of random environments.) This generalizes the computation done by J.-P. Ramis for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between integrals on cones and on domains.