Fractional weight multiplier systems on SU(d,1)

TL;DR

This paper proves that for certain arithmetic subgroups of SU(d,1), there exist finite index subgroups that lift to n-fold covers, enabling the construction of fractional weight multiplier systems.

Contribution

It establishes the existence of subgroups with fractional weight multiplier systems on SU(d,1), extending the theory of automorphic forms and multiplier systems.

Findings

Existence of finite index subgroups lifting to n-fold covers

Construction of multiplier systems of weight 1/n

Application to arithmetic subgroups of SU(d,1)

Abstract

For a class of arithmetic subgroups $\Gamma$ in SU(d,1) we prove that for every positive integer $n$ there exists a subgroup $\Gamma_n$ of finite index in $\Gamma$, which lifts to the $n$-fold connected cover of of SU(d,1). Consequently $\Gamma_n$ has a multiplier system of weight $\frac{1}{n}$.