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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Weighted projective spaces and minimal nilpotent orbits
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by Carlo A. Rossi PDF
Represent. Theory 12 (2008), 208-224 Request permission

Abstract:

We investigate (twisted) rings of differential operators on the resolution of singularities of an irreducible component $\overline X$ of $\overline O_{\mathrm {min}}\cap \mathfrak n_+$ (where $\overline O_{\mathrm {min}}$ is the (Zariski) closure of the minimal nilpotent orbit of $\mathfrak {sp}_{2n}$ and $\mathfrak n_+$ is the Borel subalgebra of $\mathfrak {sp}_{2n}$) using toric geometry, and show that they are homomorphic images of a certain family of associative subalgebras of $U(\mathfrak {sp}_{2n})$, which contains the maximal parabolic subalgebra $\mathfrak p$ determining $\overline O_{\min }$. 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 $\mathfrak {sp}_{2n}$.
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Additional Information
  • Carlo A. Rossi
  • Affiliation: Department of mathematics, ETH Zürich, 8092 Zürich, Switzerland
  • Email: crossi@math.ethz.ch
  • Received by editor(s): August 17, 2007
  • Received by editor(s) in revised form: November 8, 2007
  • Published electronically: April 17, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 12 (2008), 208-224
  • MSC (2000): Primary 13N10
  • DOI: https://doi.org/10.1090/S1088-4165-08-00328-2
  • MathSciNet review: 2403559