Hecke Operators on Vector-Valued Modular Forms

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Authors: Bouchard, V., Creutzig, T., Joshi, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210181
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Hecke Operators on Vector-Valued Modular Forms / V. Bouchard, T. Creutzig, A. Joshi // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 35 назв. — англ.

We study Hecke operators on vector-valued modular forms for the Weil representation ρL of a lattice L. We first construct Hecke operators Tᵣ that map vector-valued modular forms of type ρL into vector-valued modular forms of type ρL₍ᵣ₎, where L(r) is the lattice L with rescaled bilinear form (⋅,⋅)ᵣ...