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February 12, 2024Open Access

The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group

Puntos clave

The Siegel modular group represents the lattice with the smallest covolume in the symplectic group.
It was shown that up to conjugation, this lattice is unique among other groups.
The proof focuses on the relation between the symplectic groups over rational and real numbers and their respective lattices involved in geometry and algebra contexts. The implication highlights the structural significance of these groups in mathematical systems.

Resumen

Let n 2. We prove that, up to conjugation, Sp₂₍ (Z) is the lattice in Sp₂₍ (R) which has the smallest covolume.

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Cite This Study

Džambić et al. (Mon,) studied this question.

synapsesocial.com/papers/68e79970b6db6435877096cc https://doi.org/https://doi.org/10.48550/arxiv.2402.07604

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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On the Minimal Size of a Generating Set of Lattices in Lie Groups2020
2Formal Siegel modular forms for arithmetic subgroups2024
3On the supersingular locus of the Siegel modular variety of genus 3 or 42024
4A criterion for modularity of the subgroup lattice of a finite soluble group2024
5The cone conjecture for vector-valued Siegel automorphic forms2024

El Grupo Modular de Siegel es la Red de Covolumen Mínimo en el Grupo Simpléctico | Synapse