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Rankin-Cohen Brackets for Hermitian Jacobi Forms and Hermitian Modular FormsMartin, James D. (James Dudley) 12 1900 (has links)
In this thesis, we define differential operators for Hermitian Jacobi forms and Hermitian modular forms over the Gaussian number field Q(i). In particular, we construct Rankin-Cohen brackets for such spaces of Hermitian Jacobi forms and Hermitian modular forms. As an application, we extend Rankin's method to the case of Hermitian Jacobi forms. Finally we compute Fourier series coefficients of Hermitian modular forms, which allow us to give an example of the first Rankin-Cohen bracket of two Hermitian modular forms. In the appendix, we provide tables of Fourier series coefficients of Hermitian modular forms and also the computer source code that we used to compute such Fourier coefficients.
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Opérateurs de Rankin-Cohen et matrices de fusion / Rankin-Cohen Operators and fusion matricesMedina luna, Manuel Jair 26 January 2016 (has links)
Ce travail est consacré a l'étude des déformations covariantes des orbites co-adjointes du groupe de Lie SL(2,R).Nous établissons un lien entre des méthodes de quantification basées sur les crochets de Rankin-Cohen et les matrices de fusion pour les modules de Verma. Par ailleurs nous formalisons et étudions la notion associée d'algèbre de Rankin-Cohen qui contrôle l'associativité de ces déformations. / This work is devoted to the study of covariant star-product on coadjointorbits of the Lie group SL(2,R). We establish a correspondence between two quantization methods. The first is based on the Rankin-Cohen brackets and the second is based in the canonical element associate to the Shapovalov form and fusion matrices for Verma modules.Furthermore we formalize and study the associated notion of non-commutative algebra that controls the associativity of these deformations.
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