On Atkin-Lehner correspondences on Siegel spaces

Document Type : Special Issue of BIMS in Honor of Professor Freydoon Shahidi



‎We introduce a higher dimensional Atkin-Lehner theory for‎ ‎Siegel-Parahoric congruence subgroups of $GSp(2g)$‎. ‎Old‎ ‎Siegel forms are induced by geometric correspondences on Siegel‎ ‎moduli spaces which commute with almost all local Hecke algebras‎. ‎We also introduce an algorithm to get equations for moduli spaces of‎ ‎Siegel-Parahoric level structures‎, ‎once we have equations for prime levels and square prime levels‎ ‎over the level one Siegel space‎. ‎This way we give equations for an infinite tower of Siegel spaces‎ ‎after N‎. ‎Elkies who did the genus one case‎. 


Main Subjects

Volume 43, Issue 4 (Special Issue)
August 2017
Pages 337-359
  • Receive Date: 15 May 2017
  • Revise Date: 01 October 2017
  • Accept Date: 19 May 2017
  • First Publish Date: 01 August 2017