Twisted GGP Problems and Conjectures

TL;DR

This paper explores a twisted variant of restriction problems for classical groups, extending previous conjectures to a specific case involving skew-Hermitian spaces, and relates these to the Langlands correspondence.

Contribution

It introduces a twisted version of restriction conjectures for classical groups, focusing on a case with skew-Hermitian spaces, expanding the scope of earlier work.

Findings

Formulation of twisted restriction problems for classical groups.

Extension of conjectures to skew-Hermitian space pairs.

Connections established with Langlands correspondence.

Abstract

In an earlier work, we considered a family of restriction problems for classical groups (over local and global fields) and proposed precise answers to these problems using the local and global Langlands correspondence. These restriction problems were formulated in terms of a pair $W \subset V$ of orthogonal, Hermitian, symplectic, or skew-Hermitian spaces. In this paper, we consider a twisted variant of these conjectures in one particular case -- that of a pair of skew-Hermitian spaces $W = V$.