Abstract We calculate, in the framework of geometric Langlands program, periods cuspidal automorphic sheaves for $\operatorname{GL}_{2n}$ along Levi subgroup $\operatorname{GL}_n\times \operatorname{GL}_n$. also solve corresponding local problem.

In this article we propose a geometric description of Arthur packets for $p$-adic groups using vanishing cycles perverse sheaves. Our approach is inspired by the 1992 book Adams, Barbasch and Vogan on Langlands classification admissible representations real follows direction indicated in his 1993 paper correspondence. Using cycles, introduce study functor from category equivariant sheaves modul...

In the late 1960’s, Robert Langlands introduced a number of ideas to the theory of automorphic forms and formulated a number of conjectures which gave the theory a new focus. I was a colleague of his at this time, and a good deal of my professional energy since then has been directed to problems posed by him. Thus it was not entirely inappropriate that when I was invited to this conference, Miy...