We develop the theory of “Weyl group multiple Dirichlet series” for root systems of type C. For an arbitrary root system of rank r and a positive integer n, these are Dirichlet series in r complex variables with analytic continuation and functional equations isomorphic to the associated Weyl group. In type C, they conjecturally arise from the Fourier-Whittaker coefficients of minimal parabolic ...

In this paper, we construct explicit eigenfunctions of the local Weil representation on unitary group of one variable in the p-adic case where p is odd. The idea is to use the lattice model, and the results will be used to compute special values of certain Hecke L-functions in separated papers. We also recover Moen’s results on when a local theta lifting from U(1) to itself does not vanish. 0. ...

We investigate the formulation of Vasiliev's four-dimensional higher-spin gravity in operator form, without making reference to one specific ordering. More precisely, we make use one-to-one mapping between operators and symbols thereof for a family ordering prescriptions that interpolate go beyond Weyl normal orderings. This correspondence allows us perturbatively integrate Vasiliev system form...