Skip to Main Content

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
HTML articles powered by AMS MathViewer

by Carlo A. Rossi
Represent. Theory 12 (2008), 208-224
DOI: https://doi.org/10.1090/S1088-4165-08-00328-2
Published electronically: April 17, 2008

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 $\mathfrak {sp}_{2n}$.
References
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 13N10
  • Retrieve articles in all journals with MSC (2000): 13N10
Bibliographic 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