Rankin-Cohen Deformations and Representation Theory
Yi-Jun Yao
TL;DR
This paper explores the connection between Rankin-Cohen brackets and the representation theory of SL(2,R), providing new insights into deformation problems in modular forms and establishing key uniqueness results.
Contribution
It introduces a novel interpretation of Rankin-Cohen brackets via unitary representation theory, advancing the understanding of deformation problems in modular forms.
Findings
Established two key uniqueness theorems for deformation problems
Linked Rankin-Cohen brackets to SL(2,R) representation theory
Provided new methods for studying modular form deformations
Abstract
In this paper, we use the unitary representation theory of 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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra