Weighted projective spaces and minimal nilpotent orbits

Author:
Carlo A. Rossi

Journal:
Represent. Theory **12** (2008), 208-224

MSC (2000):
Primary 13N10

DOI:
https://doi.org/10.1090/S1088-4165-08-00328-2

Published electronically:
April 17, 2008

MathSciNet review:
2403559

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Abstract: We investigate (twisted) rings of differential operators on the resolution of singularities of an irreducible component of (where is the (Zariski) closure of the minimal nilpotent orbit of and is the Borel subalgebra of ) using toric geometry, and show that they are homomorphic images of a certain family of associative subalgebras of , which contains the maximal parabolic subalgebra determining . 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 .

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Additional Information

**Carlo A. Rossi**

Affiliation:
Department of mathematics, ETH Zürich, 8092 Zürich, Switzerland

Email:
crossi@math.ethz.ch

DOI:
https://doi.org/10.1090/S1088-4165-08-00328-2

Received by editor(s):
August 17, 2007

Received by editor(s) in revised form:
November 8, 2007

Published electronically:
April 17, 2008

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.