Proof of the Aubert-Baum-Plymen-Solleveld conjecture for split classical groups

TL;DR

This paper proves the Aubert-Baum-Plymen-Solleveld conjecture for split classical groups and links it to the Langlands correspondence, advancing understanding of representation theory and Langlands parameters.

Contribution

It establishes the conjecture for split classical groups and clarifies the relationship with the Langlands correspondence, building on previous notions of cuspidality.

Findings

Proof of the conjecture for split classical groups

Connection established with the Langlands correspondence

Enhanced Langlands parameters and cuspidal support clarified

Abstract

In this paper we prove the Aubert-Baum-Plymen-Solleveld conjecture for the split classical groups and establish the connection with the Langlands correspondence. To do this, we review the notion of cuspidality for enhanced Langlands parameters and also review the notion of cuspidal support for enhanced Langlands parameters for split classical groups, both introduced by the author in earlier work.