The Lie theory of the Rankin-Cohen brackets and allied bi-differential operators

DOI10.1016/j.aim.2005.12.002zbMath1161.11331OpenAlexW1977091283MaRDI QIDQ855501

Amine M. El Gradechi

Publication date: 7 December 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2005.12.002

zbMATH Keywords

automorphic formsVerma modulesHilbert modular formssingular vectorsinvariant theorydiscrete series representationsRankin-Cohen bracketstransvectants

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Holomorphic modular forms of integral weight (11F11) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items

Differential symmetry breaking operators. II: Rankin-Cohen operators for symmetric pairs ⋮ Rankin-Cohen brackets, transvectants and covariant differential operators ⋮ The Lie theory of the Rankin-Cohen brackets and allied bi-differential operators ⋮ Covariant bi-differential operators on matrix space ⋮ The Lie theory of certain modular form and arithmetic identities ⋮ Rankin-Cohen brackets and representations of conformal Lie groups ⋮ Invariants of formal pseudodifferential operator algebras and algebraic modular forms ⋮ Ramanujan systems of Rankin-Cohen type and hyperbolic triangles ⋮ Singular invariant trilinear forms and covariant (bi-)differential operators under the conformal group ⋮ A geometric interpretation and explicit form for higher-order Hankel operators ⋮ Rankin-Cohen deformations and representation theory ⋮ Formal deformations of the algebra of Jacobi forms and Rankin-Cohen brackets ⋮ Rankin-Cohen brackets and associativity ⋮ Combinatorics of Maass-Shimura operators ⋮ Covariant quantization: spectral analysis versus deformation theory

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