Dani Szpruch : Casselman-Shalika formula for the similitude metaplectic group

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

Nov. 13, 2013, 11 a.m.

In

SEO 1227

Abstract

In this talk we shall survey the construction of genuine principal series representations of covering groups and their Whittaker functionals emphasizing the differences between the linear and the metaplectic cases. We shall then move to the special case of the metaplectic double cover of GSp(2n,F). We shall present a symmetric Casselman-Shalika formula for this group exploiting the uniqueness of Whittaker model for the metaplectic double cover of Sp(2n,F) and a surprising connection between representation theory of these two groups. As an application we shall describe a family of reducible unitary unramified principal series representations.

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