Group, Lie and Number Theory

Shahidi local coefficients associated with parabolic inductions on quasi-split reductive groups defined over a local field are the core of the Langlands-Shahidi method. These meromorphic invariants arise from the uniqueness of Whittaker model. Among their local applications one finds irreducibility results and a formula for Plancherel measures. In the context of metaplectic groups, uniqueness of Whittaker model does not hold anymore. Yet, an analog for these coefficients exists. This analog goes back to Kazhdan-Patterson seminal work on the exceptional representations and is often referred to as a scattering matrix. In this talk we shall give new and simple interpretation to these matrices for coverings of p-adic SL(2) and relate them to Tate-type gamma factors. We shall also give some local applications. This talk should be accessible also for non-experts. Speaker(s): Dani Szpruch (Howard University)