Raising the level of automorphic representations of $\mathrm{GL}_{2n}$ of unitary type

TL;DR

This paper utilizes the endoscopic classification of automorphic representations of even-dimensional unitary groups to develop level-raising congruences, advancing the understanding of automorphic forms and their congruences.

Contribution

It introduces a novel method for constructing level-raising congruences for automorphic representations of $ ext{GL}_{2n}$ of unitary type using endoscopic classification.

Findings

Constructed explicit level-raising congruences

Extended the endoscopic classification framework

Enhanced understanding of automorphic representations

Abstract

We use the endoscopic classification of automorphic representations of even-dimensional unitary groups to construct level-raising congruences.