A calculation of a half-integral weight multiplier system on SU(2,1)

TL;DR

This paper constructs a half-integral weight multiplier system on SU(2,1) by deriving a 2-cocycle for its double cover over local fields and analyzing its splitting on compact subgroups.

Contribution

It provides an explicit formula for the 2-cocycle and describes the local splitting behavior, advancing the understanding of multiplier systems on SU(2,1).

Findings

Derived a formula for the 2-cocycle of the double cover.

Described the splitting of the cocycle on compact open subgroups.

Expressed the multiplier system as a product of local splittings.

Abstract

In this thesis, we construct a half-integral weight multiplier system on the group SU(2,1). In order to do so, we first find a formula for a 2-cocycle representing the double cover of SU(2,1)(k), where k is a local field. For each non-archimedean local field k, we describe how the cocycle splits on a compact open subgroup. The multiplier system is then expressed in terms of the product of the local splittings at each prime.