Solomon Friedberg (Boston College)

The classical Shimura correspondence lifts automorphic representations on the double cover of SL(2), corresponding to classical half-integral weight forms, to automorphic representations on PGL(2). Though efforts have been made for many years to generalize this map to higher rank groups and higher degree covers, our knowledge is limited. In this talk I present joint work with Omer Offen that  points to a new Shimura lift for automorphic representations on the triple cover of SL(3).  We establish the Fundamental Lemma for a relative trace formula.  Moreover, this project will characterize the image of the lift by means of a period involving a theta function on SO(8), confirming a 2001 conjecture of Bump, Friedberg and Ginzburg.