- Definition
- References
In mathematics, an Igusa group or Igusa subgroup is a subgroup of the Siegel modular group defined by some congruence conditions. They were introduced by {{harvs|txt|last=Igusa|authorlink=Jun-Ichi Igusa|year=1964}}.
Definition
The symplectic group Sp2g(Z) consists of the matrices
such that ABt and CDt are symmetric, and ADt − CBt = I (the identity matrix).
The Igusa group Γg(n,2n) = Γn,2n consists of the matrices
in Sp2g(Z) such that B and C are congruent to 0 mod n, A and D are congruent to the identity matrix I mod n, and the diagonals of ABt and CDt are congruent to 0 mod 2n.
We have Γg(2n)⊆ Γg(n,2n) ⊆ Γg(n) where Γg(n) is the subgroup of matrices congruent to the identity modulo n.
References
- {{citation|mr=0164967
|last=Igusa|first= Jun-ichi
|title=On the graded ring of theta-constants
|journal=Amer. J. Math.|volume= 86 |year=1964|pages= 219–246|doi=10.2307/2373041}}
1 : Automorphic forms
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