Supercuspidal L-packets via isocrystals

TL;DR

This paper extends the construction of supercuspidal L-packets from pure to non-pure inner forms of unramified p-adic groups using isocrystals, establishing their stability and endoscopic transfer.

Contribution

It introduces a new method based on isocrystals for constructing supercuspidal L-packets on non-pure inner forms, generalizing previous work.

Findings

Construction of L-packets for non-pure inner forms.

Proof of stability and endoscopic transfer properties.

Extension of existing theories to broader classes of p-adic groups.

Abstract

In a recent paper, DeBacker and Reeder construct and parameterize L-packets on pure inner forms of unramified p-adic groups, that consist of depth zero supercuspidal representations. We generalize their work to non-pure inner forms, by providing an alternative construction based on the theory of isocrystals with additional structure due to Kottwitz. Furthermore, we show the stability and endoscopic transfer for these L-packets.