College of Liberal Arts & Sciences

# Mathematics Colloquium - Dani Szpruch

**Abstract:** Langlands Shahidi method is one of the two main approaches for defining and studying automorphic *L*-functions. This method is centered around Shahidi local coefficients which are analytic invariants associated with certain induced representations on linear groups. These coefficients arise from a uniqueness result known as uniqueness of Whittaker model. Among the local applications of these coefficients one finds irreducibility results and a formula for Plancherel measures. In the context of metaplectic groups, which are non-linear covering groups, uniqueness of Whittaker model does not hold anymore. Yet, an analog for these coefficients exists, dating back to Kazhdan-Patterson seminal work on the theta representations. In this talk we shall give new and simple interpretation to this analog for coverings of *p*-adic *SL*(2) and relate them to Tate gamma factors. We shall also give some local applications.