Descent Construction for Gspin Groups: Main Results and Applications

TL;DR

This paper extends the descent method for Gspin groups to essentially self dual representations, complementing recent advances in transfer and cuspidality results for automorphic representations.

Contribution

It introduces an extension of the descent construction for Gspin groups applicable to essentially self dual representations, enhancing existing transfer and cuspidality theories.

Findings

Extension of descent method for Gspin groups

Complement to recent transfer results by Asgari and Shahidi

Supports cuspidality of exterior square lifts for GL4

Abstract

The purpose of this note is to announce an extension of the descent method of Ginzburg, Rallis and Soudry to the setting of essentially self dual representations. This extension of the descent construction provides a complement to recent work of Asgari and Shahidi on the generic transfer for general Spin groups as well as to the work of Asgari and Raghuram on cuspidality of the exterior square lift for representations of GL4. Complete proofs of the results announced in the present note will appear in our forthcoming articles.