Multiplying Modular Forms

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dc.creatorWeissman, Martin H.
dc.date2006-11-30
dc.date2007-04-09
dc.date.accessioned2026-07-07T07:55:37Z
dc.date.available2026-07-07T07:55:37Z
dc.descriptionThe 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 directly yielding a ring structure on some spaces of modular forms. We discuss discrete decomposability, and its role in constructing ring structures.
dc.description22 pages. v2. One serious flaw and numerous typos fixed
dc.identifierhttps://arxiv.org/abs/math/0612004
dc.identifierhttp://arxiv.org/abs/math/0612004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127032
dc.subjectRepresentation Theory
dc.subjectNumber Theory
dc.subject11F70, 22E46
dc.titleMultiplying Modular Forms
dc.typetext

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