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 Igusa (1964).
Definition
The symplectic group Sp2g(Z) consists of the matrices
such that ABt and CDt are symmetric, and ADt − CDt = 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
Igusa group Wikipedia(Text) CC BY-SA