Local Langlands Conjecture for $p$-adic $GSpi{n}_4,$ $GSpi{n}_6,$ and their inner forms

Abstract

We establish the local Langlands conjecture for small rank general spin groups $GSpi{n}_4$ and $GSpi{n}_6$ 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.

the description of the group structure of the central extension, all the sizes of L-packets for GSpin(4) and its non quasi-split F-inner forms, and their multiplicity in restriction added; exposition improved

References in corpus (2)

• Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations
• Dual R-groups of the inner forms of SL(N)

Cited by in corpus (2)

• On the global Gan-Gross-Prasad conjecture for general spin groups
• Representations of the $p$-Adic $GSpi{n}_4$ and $GSpi{n}_6$ and the Adjoint L-Function