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

2024/02/12 by Džambić, Amir, Holm, Kristian, Köhl, Ralf · 1 citation
#20G30 #22E40 (Primary) 1E57 #51M25 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.07604

Abstract

Let n \geqslant 2. We prove that, up to conjugation, Sp_2n (Z) is the unique lattice in Sp_2n (R) of the smallest covolume.

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• Finiteness of Free Algebras of Modular Forms on Unitary Groups

Related

• Siegel modular forms and finite symplectic groups
• Siegel modular forms associated to Weil representations
• Non-commutative covers and the modular group
• Abelian subgroups and semisimple elements in 2-modular representations\n of the symplectic group Sp_2n(2)
• Coset representatives corresponding to Yetter-Drinfeld modules of modular group and continued fraction