Paramodular group

random Wiki of the Day

rWotD Episode 2700: Paramodular group
Welcome to Random Wiki of the Day, your journey through Wikipedia’s vast and varied content, one random article at a time.
The random article for Tuesday, 24 September 2024 is Paramodular group.
In mathematics, a paramodular group is a special sort of arithmetic subgroup of the symplectic group. It is a generalization of the Siegel modular group, and has the same relation to polarized abelian varieties that the Siegel modular group has to principally polarized abelian varieties. It is the group of automorphisms of Z2n preserving a non-degenerate skew symmetric form. The name "paramodular group" is often used to mean one of several standard matrix representations of this group. The corresponding group over the reals is called the parasymplectic group and is conjugate to a (real) symplectic group. A paramodular form is a Siegel modular form for a paramodular group.
Paramodular groups were introduced by Conforto (1952) and named by Shimura (1958, section 8).
This recording reflects the Wikipedia text as of 00:36 UTC on Tuesday, 24 September 2024.
For the full current version of the article, see Paramodular group on Wikipedia.
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