Skip to Main Content

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.

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.


Differential operators on some nilpotent orbits
HTML articles powered by AMS MathViewer

by T. Levasseur and J. T. Stafford PDF
Represent. Theory 3 (1999), 457-473 Request permission


In recent work, Astashkevich and Brylinski construct some differential operators of Euler degree $-1$ (thus, they lower the degree of polynomials by one) on the coordinate ring $\mathcal {O}(\mathbb {O}_{\min }(\mathfrak {g}))$ of the minimal nilpotent orbit $\mathbb O_{\min }(\mathfrak {g})$ for any classical, complex simple Lie algebra $\mathfrak {g}$. They term these operators “exotic” since there is “(apparently) no geometric or algebraic theory that explains them”. In this paper, we provide just such an algebraic theory for ${\mathfrak {sl}}(n)$ by giving a complete description of the ring of differential operators on $\mathbb O_{\min }({\mathfrak {sl}}(n)).$ The method of proof also works for various related varieties, notably for the Lagrangian submanifolds of the minimal orbit of classical Lie algebras for which Kostant and Brylinski have constructed exotic differential operators.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (1991): 14L30, 16S32, 17B20, 58F06
  • Retrieve articles in all journals with MSC (1991): 14L30, 16S32, 17B20, 58F06
Additional Information
  • T. Levasseur
  • Affiliation: Département de Mathématiques, Université de Brest, 29285 Brest, France
  • Email:
  • J. T. Stafford
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • Email:
  • Received by editor(s): September 7, 1999
  • Received by editor(s) in revised form: October 13, 1999
  • Published electronically: December 3, 1999
  • Additional Notes: The research of both authors was supported in part by NSF grant NSF-G-DMS 9801148
  • © Copyright 1999 American Mathematical Society
  • Journal: Represent. Theory 3 (1999), 457-473
  • MSC (1991): Primary 14L30, 16S32, 17B20, 58F06
  • DOI:
  • MathSciNet review: 1719509