Theta correspondence and Arthur packets: on the Adams conjecture

TL;DR

This paper investigates the Adams conjecture, which posits that the local theta correspondence preserves Arthur packets, specifically focusing on symplectic--even orthogonal dual pairs, and clarifies when the conjecture is valid.

Contribution

It offers a detailed analysis of the conditions under which the Adams conjecture holds for symplectic--even orthogonal dual pairs.

Findings

Identifies cases where the Adams conjecture is valid.

Provides a precise description of the correspondence in these cases.

Clarifies the limitations of the conjecture's applicability.

Abstract

The Adams conjecture predicts that the local theta correspondence should respect Arthur packets. In this paper, we revisit the Adams conjecture for the symplectic--even orthogonal dual pair. Our results provide a precise description of all situations in which the conjecture holds.