The Langlands-Shahidi Method for the metaplectic group and applications

TL;DR

This paper extends the Langlands-Shahidi method to the metaplectic double cover of Sp(2n), establishing key properties like Whittaker model uniqueness, local coefficients, and gamma factors, with applications to representation theory.

Contribution

It introduces the Langlands-Shahidi method for the metaplectic group, proving Whittaker model uniqueness and defining local coefficients and gamma factors.

Findings

Whittaker model of irreducible admissible representations is unique

Local coefficients for the metaplectic group are defined and analyzed

Connections with the representation theory of SO(2n+1) are established

Abstract

I am applying the Langlands-Shahidi method to the metaplectic double cover of Sp(2n). I proved that a Whittaker model of an irreducible admissible representation of this group is unique. As a result I was able to define the local coefficients for this group. I used them to determine irreducibility of parabolic induction. I also found some connections with the representation theory of SO(2n+1). I have defined local gamma factors and proved some properties of them.