Two Identities relating Eisenstein series on classical groups

TL;DR

This paper introduces two new identities connecting Eisenstein series on classical groups and their covers, extending previous constructions like doubling and descent methods to broader contexts.

Contribution

It presents two general identities that unify and extend existing constructions of Eisenstein series on classical groups and their covers.

Findings

Extended the doubling construction to new settings.

Generalized the descent construction for classical groups.

Provided new identities linking Eisenstein series and covers.

Abstract

In this paper we introduce two general identities relating Eisenstein series on split classical groups, as well as double covers of symplectic groups. The first identity can be viewed as an extension of the doubling construction introduced in [CFGK17]. The second identity is a generalization of the descent construction studied in [GRS11].