L-packets over strong real forms

TL;DR

This paper proves the equivalence of two different constructions of combined L-packets over all real forms of a reductive group, refining the local Langlands correspondence.

Contribution

It establishes that Adams-Barbasch-Vogan's and Kaletha's definitions of combined L-packets are identical and share the same parameterization.

Findings

Proved the equivalence of two L-packet constructions

Confirmed the parameterization consistency of both methods

Refined the understanding of the local Langlands correspondence

Abstract

Langlands defined L-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan combined L-packets over all real forms belonging to an inner class. Using different methods, Kaletha also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.