A note on a fundamental domain for Siegel-Jacobi space

TL;DR

This paper investigates the structure of a fundamental domain for the Siegel-Jacobi space, which combines symplectic and Heisenberg group actions on complex spaces, contributing to the understanding of its geometric and arithmetic properties.

Contribution

It provides a detailed analysis of a fundamental domain for the Siegel-Jacobi space, enhancing the understanding of its geometric structure and symmetry properties.

Findings

Description of a fundamental domain for the Siegel-Jacobi space

Insights into the symmetry and geometric structure of the space

Potential applications to automorphic forms and number theory

Abstract

In this paper, we study a fundamental domain for the Siegel-Jacobi space $Sp(g,{\mathbb Z})\ltimes H_{\mathbb Z}^{(g,h)}\backslash {\mathbb H}_g\times {\mathbb C}^{(h,g)}$.