Jacobi group

In mathematics, the Jacobi group, introduced by Eichler & Zagier (1985), is the semidirect product of the symplectic group Sp_2n(R) and the Heisenberg group R¹⁺²ⁿ. The concept is named after Carl Gustav Jacob Jacobi. Automorphic forms on the Jacobi group are called Jacobi forms.

References

• Berndt, Rolf; Schmidt, Ralf (1998), Elements of the representation theory of the Jacobi group, Progress in Mathematics, vol. 163, Birkhäuser Verlag, ISBN 978-3-7643-5922-5, MR 1634977
• Eichler, Martin; Zagier, Don (1985), The theory of Jacobi forms, Progress in Mathematics, vol. 55, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3180-2, MR 0781735