Linear periods of automorphic sheaves for GL_{2n}

TL;DR

This paper computes the periods of cuspidal automorphic sheaves for GL_{2n} within the geometric Langlands framework, addressing both global and local aspects of the problem.

Contribution

It provides a calculation of automorphic sheaf periods for GL_{2n} and solves the related local problem, advancing the understanding of automorphic sheaves in geometric Langlands.

Findings

Explicit calculation of periods for GL_{2n} automorphic sheaves

Solution to the local period problem for GL_{2n}

Progress in geometric Langlands program understanding

Abstract

We calculate, in the framework of the geometric Langlands program, the periods of cuspidal automorphic sheaves for GL_{2n} along the Levi subgroup GL_n\times\GL_n. We also solve the corresponding local problem.