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in creator/contributor: "Conley, Charles H."  
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Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

Description: Let G be a Lie group acting on a homogeneous space G/K. The center of the universal enveloping algebra of the Lie algebra of G maps homomorphically into the center of the algebra of differential operators on G/K invariant under the action of G. In the case that G is a Jacobi Lie group of rank 2, we prove that this homomorphism is surjective and hence that the center of the invariant differential operator algebra is the image of the center of the universal enveloping algebra. This is an extensio… more
Date: August 2013
Creator: Dahal, Rabin
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Rankin-Cohen Brackets for Hermitian Jacobi Forms and Hermitian Modular Forms

Description: 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 Her… more
Date: December 2016
Creator: Martin, James D. (James Dudley)
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Non-Resonant Uniserial Representations of Vec(R)

Description: The non-resonant bounded uniserial representations of Vec(R) form a certain class of extensions composed of tensor density modules, all of whose subquotients are indecomposable. The problem of classifying the extensions with a given composition series is reduced via cohomological methods to computing the solution of a certain system of polynomial equations in several variables derived from the cup equations for the extension. Using this method, we classify all non-resonant bounded uniserial ext… more
Date: May 2018
Creator: O'Dell, Connor
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Uniserial Representations of Vec(R) with a Single Casimir Eigenvalue

Description: In 1980 Feigin and Fuchs classified the length 2 bounded representations of Vec(R), the Lie algebra of polynomial vector fields on the line, as a result of their work on the cohomology of Vec(R). This dissertation is concerned mainly with the uniserial (completely indecomposable) representations of Vec(R) with a single Casimir eigenvalue and weights bounded below. Such representations are composed of irreducible representations with semisimple Euler operator action, bounded weight space dimensi… more
Date: May 2018
Creator: Kuhns, Nehemiah
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Hochschild Cohomology and Complex Reflection Groups

Description: A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the se… more
Date: August 2012
Creator: Foster-Greenwood, Briana A.
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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Hermitian Jacobi Forms and Congruences

Description: In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.
Date: August 2014
Creator: Senadheera, Jayantha
Item Type: Refine your search to only Thesis or Dissertation
Partner: UNT Libraries
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