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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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.