The symplectic geometry of a new kind of Siegel upper half space of order 2 (I)

TL;DR

This paper introduces a novel Siegel upper half space of order 2, exploring its symplectic geometry and group actions, laying groundwork for future number theoretic applications.

Contribution

It defines a new type of Siegel upper half space and analyzes its symplectic geometry under holomorphic transformations, providing foundational insights for subsequent number theory work.

Findings

Explicit symplectic geometric structure established

Group actions of holomorphic transformations characterized

Framework set for future number theoretic applications

Abstract

In this paper, we introduce a new kind of Siegel upper half space and consider the symplectic geometry on it explicitly under the action of the group of all holomorphic transformations of it. The results and methods will form a basis for our number theoretic applications later.