Local Langlands Conjecture for $p$-adic $GSpin_4,$ $GSpin_6,$ and their inner forms

TL;DR

This paper proves the local Langlands conjecture for specific small rank GSpin groups and their inner forms, constructing L-packets and analyzing their properties and sizes.

Contribution

It establishes the local Langlands correspondence for GSpin_4 and GSpin_6, including construction and characterization of L-packets for these groups.

Findings

Constructed L-packets for GSpin_4 and GSpin_6

Verified properties of L-packets aligned with local factors

Determined sizes of L-packets in many cases

Abstract

We establish the local Langlands conjecture for small rank general spin groups $GSpin_4$ and $GSpin_6$ as well as their inner forms. We construct appropriate $L$-packets and prove that these $L$-packets satisfy the properties expected of them to the extent that the corresponding local factors are available. We are also able to determine the exact sizes of the $L$-packets in many cases.