  We define a multiple Dirichlet series associated with quadrics which is the
zero locus of a quadratic form. This multiple Dirichlet series is linked to a
Shintani zeta function associated with a prehomogeneous vector space. To obtain
the functional equations we construct a filtration of the quadratic space and
define the parabolic group actions, and then apply a non-abelian Poisson
summation formula which sums over all lower dimensional quadrics along with the
original quadrics. We show the group of functional equations is isomorphic to a
finite Weyl group of type A3.
