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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Weighted projective spaces and minimal nilpotent orbits
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by Carlo A. Rossi
Represent. Theory 12 (2008), 208-224
Published electronically: April 17, 2008


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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Bibliographic Information
  • Carlo A. Rossi
  • Affiliation: Department of mathematics, ETH Zürich, 8092 Zürich, Switzerland
  • Email:
  • 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:
  • MathSciNet review: 2403559