Functoriality and the theta correspondence

TL;DR

This paper investigates the functoriality of the local theta correspondence for classical p-adic groups, adapting the Adams conjecture to ABV-packets and providing evidence particularly for general linear groups.

Contribution

It introduces a new approach to studying the functoriality of the local theta correspondence using the adaptation of the Adams conjecture to ABV-packets.

Findings

Evidence supporting the conjecture in the case of general linear groups.

Development of a framework connecting the Adams conjecture with ABV-packets.

Advancement in understanding the functoriality of local theta correspondence.

Abstract

We study the functoriality of the local theta correspondence for classical $p$-adic groups. This is realized via the adaptation of the Adams conjecture to ABV-packets. We provide evidence for the conjecture, especially in the case of general linear groups.