A computation of the gamma matrix of a family of \(p\)-adic zeta integrals
The purpose of this paper is to compute the \(\gamma\)-matrices which occur in the functional equation for the \(p\)-adic zeta integral on the space of \(n\times n\) symmetric matrices over a non-archimedean field of characteristic 0. It is a typical and important example of the computation of \(\gamma\)-matrices associated with regular prehomogeneous vector spaces. The authors also gives some applications to computing the points of reducibility of certain families of degenerate principal series representations of classical groups, to the study of Eisenstein series on these same groups and to non-vanishing of theta lifts.
scientific article; zbMATH DE number 844633