Journal of Lie Theory

no. 3
The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group
Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 527-556
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.
DOI: 10.5802/jolt.1395
Classification: 22E40, 11E57, 20G30, 51M25
Keywords: Symplectic group, arithmetic group, lattice, covolume, Prasad's volume formula 
@article{JOLT_2025_35_3_a3,
     author = {A. Dzambic and K. Holm and R. Koehl},
     title = {The {Siegel} {Modular} {Group} is the {Lattice} of {Minimal} {Covolume} in the {Symplectic} {Group}},
     journal = {Journal of Lie Theory},
     pages = {527--556},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1395},
     zbl = {08103100},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1395/}
}
TY  - JOUR
AU  - A. Dzambic
AU  - K. Holm
AU  - R. Koehl
TI  - The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group
JO  - Journal of Lie Theory
PY  - 2025
SP  - 527
EP  - 556
VL  - 35
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1395/
DO  - 10.5802/jolt.1395
ID  - JOLT_2025_35_3_a3
ER  - 
%0 Journal Article
%A A. Dzambic
%A K. Holm
%A R. Koehl
%T The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group
%J Journal of Lie Theory
%D 2025
%P 527-556
%V 35
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1395/
%R 10.5802/jolt.1395
%F JOLT_2025_35_3_a3
A. Dzambic; K. Holm; R. Koehl. The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 527-556. doi: 10.5802/jolt.1395

Cited by Sources: