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- W63620599 abstract "Following Weyl’s account in The Classical Groups we develop an analogue of the (first and second) Fundamental Theorems of Invariant Theory for rings of differential operators: when V is a k-dimensional complex vector space with the standard SL kC action, we give a presentation of the ring of invariant differential operators D(C[V n])SLkC and a description of the ring of differential operators on the G.I.T. quotient, D(C[V n]SLkC), which is the ring of differential operators on the (affine cone over the) Grassmann variety of k-planes in NumberingDepth=0-dimensional space. We also compute the Hilbert series of the associated graded rings GrD(C[V n])SLk and Gr(D(C[V n]SLkC)). This computation shows that earlier claims that the kernel of themap from D(C[V n])SLkC to D(C[V n]SLkC) is generated by the Casimir operator are incorrect. Something can be gleaned from these earlier incorrect computations though: the kernel meets the universal enveloping algebra of slkC precisely in the central elements of U(slkC)." @default.
- W63620599 created "2016-06-24" @default.
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- W63620599 date "2009-11-14" @default.
- W63620599 modified "2023-09-24" @default.
- W63620599 title "Differential Operators on Grassmann Varieties" @default.
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- W63620599 doi "https://doi.org/10.1007/978-0-8176-4875-6_10" @default.
- W63620599 hasPublicationYear "2009" @default.
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