MATH - PhD Student Seminar - Spherical Hecke Algebra Actions on Weil Representations

The Weil representation is an important representation of the Metaplectic group, a double cover of the symplectic group. To study this representation, one can embed the even part into a degenerate principal series representation, which contains a spherical vector. Then one can compute the action of the metaplectic Hecke algebra on this spherical vector by a formula analogous to Macdonald’s formula on p-adic spherical functions. This method might be generalized to the case of loop groups.