Multiplying Modular Forms
Martin H. Weissman

TL;DR
This paper explores the connection between the algebraic structure of modular forms and the representation theory of real semisimple Lie groups, providing explicit constructions of intertwining operators that reflect the ring structure.
Contribution
It explicitly links the ring structure on modular forms with branching problems in representation theory and constructs a family of intertwining operators illustrating this connection.
Findings
Constructed explicit intertwining operators for discrete series representations.
Connected the ring structure of modular forms with representation branching problems.
Discussed analytic subtleties and conditions like discrete decomposability.
Abstract
The space of elliptic modular forms of fixed weight and level can be identfied with a space of intertwining operators, from a holomorphic discrete series representation of SL2(R) to a space of automorphic forms. Moreover, multiplying elliptic modular forms corresponds to a branching problem involving tensor products of holomorphic discrete series representations. In this paper, we explicitly connect the ring structure on spaces of modular forms with branching problems in the representation theory of real semisimple Lie groups. Furthermore, we construct a family of intertwining operators from discrete series representations into tensor products of other discrete series representations. This collection of intertwining operators provides the well-known ring structure on spaces of holomorphic modular forms. An analytic subtlety prevents this collection of intertwining operators from…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Finite Group Theory Research
