A multiplicity one theorem for general spin groups

Abstract: A classical problem in representation theory is how a representation of a group decomposes when restricted to a subgroup. In the 1990s, Gross-Prasad formulated an intriguing conjecture regarding the restriction of representations, also known as branching laws, of special orthogonal groups. Gan, Gross and Prasad extended this conjecture, now known as the local Gan-Gross-Prasad (GGP) conjecture, to the remaining classical groups. There are many ingredients needed to prove a local GGP conjecture. In this talk, we will focus on the first ingredient: a multiplicity at most one theorem. Aizenbud, Gourevitch, Rallis and Schiffmann proved a multiplicity (at most) one theorem for restrictions of irreducible representations of certain p-adic classical groups and Waldspurger proved the same theorem for the special orthogonal groups. We will discuss work that establishes a multiplicity (at most) one theorem for restrictions of irreducible representations for a non-classical group, the general spin group. This is joint work with Shuichiro Takeda.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar