Journal of Lie Theory 35 (2025), No. 3, 527--556
Copyright Heldermann Verlag 2025
The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group
Amir Džambic
Dept. of Mathematics, Christian-Albrechts-Universität, Kiel, Germany
dzambic@math.uni-kiel.de
Kristian Holm
Dept. of Mathematics, Christian-Albrechts-Universität, Kiel, Germany
holm@math.uni-kiel.de
Ralf Köhl
Dept. of Mathematics, Christian-Albrechts-Universität, Kiel, Germany
koehl@math.uni-kiel.de
[Abstract-pdf]
Let $n \geqslant 2$. We prove that, up to conjugation, SP$_{2n}$({\bf Z}) is the unique lattice in SP$_{2n}$({\bf R}) of the smallest covolume.
Keywords: Symplectic group, arithmetic group, lattice, covolume, Prasad's volume formula.
MSC: 22E40; 11E57, 20G30, 51M25.
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