A multiplicity one theorem for general spin groups
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 a 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.