The local Langlands conjecture for Sp(4)

TL;DR

This paper proves the local Langlands conjecture for Sp(4) by leveraging results for GSp(4), and determines the sizes of L-packets for Sp(4).

Contribution

It establishes the local Langlands conjecture for Sp(4) based on prior work for GSp(4), clarifying the structure of L-packets.

Findings

Proof of the local Langlands conjecture for Sp(4)

Determination of possible sizes of L-packets for Sp(4)

Reduction of Sp(2n) case to GSp(2n) case

Abstract

We show that the local Langlands conjecture for $Sp(2n)$ follows from that for $GSp(2n)$. In particular, we prove the local Langlands conjecture for $Sp(4)$, based on our previous work on the local Langlands conjecture for $GSp(4)$. We also determine the possible sizes of $L$-packets for $Sp(4)$.