Depth zero supercuspidal L-packets for inner forms of GSp_4

TL;DR

This paper proves that for certain parameters of GSp_4 and its inner forms, the predicted L-packets match the explicitly constructed depth zero supercuspidal packets, confirming a key aspect of the local Langlands correspondence.

Contribution

It establishes the equality of L-packets from the local Langlands conjecture with those constructed by DeBacker and Reeder for specific parameters of GSp_4 and its inner forms.

Findings

L-packets agree with DeBacker-Reeder construction

Validates the local Langlands conjecture for these cases

Connects parameters with explicit supercuspidal representations

Abstract

We show that for any tame regular discrete series parameter of GSp_4 or its inner form GU_2(D), the L-packet attached by the local Langlands conjecture agrees with the L-packet of depth zero supercuspidal representations constructed by DeBacker and Reeder.