Rankin-Cohen deformations and representation theory
نویسندگان
چکیده
منابع مشابه
Rankin-Cohen Deformations and Representation Theory
In this paper, we use the unitary representation theory of SL2(R) to understand the Rankin-Cohen brackets for modular forms. Then we use this interpretation to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.
متن کاملA Survey on Rankin-cohen Deformations
This is a survey about recent progress in Rankin-Cohen deformations. We explain a connection between Rankin-Cohen brackets and higher order Hankel forms.
متن کاملRankin-Cohen Brackets and Invariant Theory
Using maps due to Ozeki and Broué-Enguehard between graded spaces of invariants for certain finite groups and the algebra of modular forms of even weight we equip these invariants spaces with a differential operator which gives them the structure of a Rankin-Cohen algebra. A direct interpretation of the Rankin-Cohen bracket in terms of transvectant for the group SL(2,C) is given.
متن کاملSymbolic Computation for Rankin-Cohen Differential Algebras
Zagier pursues the study of the algebraic structure that this operation gives to the ring of modular forms viewed as a differential module, observing that it is “not clear how far we would have to go to get the first relation or how much further to ensure that all subsequent relations obtained would be consequences of ones already found”. Instead of determining the relations, he proposes the ab...
متن کاملRankin-Cohen Operators for Jacobi and Siegel Forms
For any non-negative integer v we construct explicitly ⌊v2⌋+1 independent covariant bilinear differential operators from Jk,m × Jk′,m′ to Jk+k′+v,m+m′ . As an application we construct a covariant bilinear differential operator mapping S (2) k ×S (2) k′ to S (2) k+k′+v. Here Jk,m denotes the space of Jacobi forms of weight k and index m and S (2) k the space of Siegel modular forms of degree 2 a...
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ژورنال
عنوان ژورنال: Chinese Annals of Mathematics, Series B
سال: 2014
ISSN: 0252-9599,1860-6261
DOI: 10.1007/s11401-014-0850-z