A characterization of the Maass space on O(2, m+2) by symmetries

TL;DR

This paper characterizes the Maass space on O(2, m+2) using symmetries of automorphic forms, providing a new perspective on its structure and relation to the Saito-Kurokawa lifting.

Contribution

It introduces specific symmetries for automorphic forms on O(2, m+2) and proves their space coincides with the Maass space, linking symmetries to automorphic form classification.

Findings

Symmetries characterize the Maass space.

Maass space equals forms satisfying these symmetries.

Connection established with Saito-Kurokawa lifting.

Abstract

In this paper, we define certain symmetries for automorphic forms on O(2, m+2) and show that the space of automorphic forms satisfying these symmetries coincides with the Maass space, the image of Saito-Kurokawa lifting.