Weighted Projective Spaces and Minimal Nilpotent Orbits
نویسنده
چکیده
We investigate (twisted) rings of differential operators on the resolution of singularities of an irreducible component X of Omin ∩ n+ (where Omin is the (Zariski) closure of the minimal nilpotent orbit of sp2n and n+ is the Borel subalgebra of sp2n) using toric geometry, and show that they are homomorphic images of a certain family of associative subalgebras of U(sp2n), which contains the maximal parabolic subalgebra p determining Omin. Further, using Fourier transforms on Weyl algebras, we show that (twisted) rings of well-suited weighted projective spaces are obtained from the same family of subalgebras. Finally, we investigate this family of subalgebras from the representation-theoretical point of view and, among other things, rediscover in a different framework irreducible highest weight modules for the UEA of sp2n.
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