Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank

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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 extension of work of Bringmann, Conley, and Richter in the rank ... continued below

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Dahal, Rabin August 2013.

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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 extension of work of Bringmann, Conley, and Richter in the rank 1case.

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  • August 2013

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  • April 23, 2014, 8:20 p.m.

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  • Nov. 16, 2016, 11:50 a.m.

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Dahal, Rabin. Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank, dissertation, August 2013; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc283833/: accessed November 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .