Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line

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Certain subquotients of Vec(R)-modules of pseudodifferential operators from one tensor density module to another are categorized, giving necessary and sufficient conditions under which two such subquotients are equivalent as Vec(R)-representations. These subquotients split under the projective subalgebra, a copy of ????2, when the members of their composition series have distinct Casimir eigenvalues. Results were obtained using the explicit description of the action of Vec(R) with respect to this splitting. In the length five case, the equivalence classes of the subquotients are determined by two invariants. In an appropriate coordinate system, the level curves of one of these invariants are a ... continued below

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Larsen, Jeannette M. August 2012.

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  • Larsen, Jeannette M.

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Certain subquotients of Vec(R)-modules of pseudodifferential operators from one tensor density module to another are categorized, giving necessary and sufficient conditions under which two such subquotients are equivalent as Vec(R)-representations. These subquotients split under the projective subalgebra, a copy of ????2, when the members of their composition series have distinct Casimir eigenvalues. Results were obtained using the explicit description of the action of Vec(R) with respect to this splitting. In the length five case, the equivalence classes of the subquotients are determined by two invariants. In an appropriate coordinate system, the level curves of one of these invariants are a pencil of conics, and those of the other are a pencil of cubics.

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  • August 2012

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  • March 4, 2013, 2:02 p.m.

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  • Nov. 16, 2016, 12:04 p.m.

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Larsen, Jeannette M. Equivalence Classes of Subquotients of Pseudodifferential Operator Modules on the Line, dissertation, August 2012; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc149627/: accessed November 19, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .