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.


Local systems on nilpotent orbits and weighted Dynkin diagrams
HTML articles powered by AMS MathViewer

by Pramod N. Achar and Eric N. Sommers
Represent. Theory 6 (2002), 190-201
Published electronically: September 5, 2002


We study the Lusztig-Vogan bijection for the case of a local system. We compute the bijection explicitly in type A for a local system and then show that the dominant weights obtained for different local systems on the same orbit are related in a manner made precise in the paper. We also give a conjecture (putatively valid for all groups) detailing how the weighted Dynkin diagram for a nilpotent orbit in the dual Lie algebra should arise under the bijection.
    achar:thesis P. N. Achar, Equivariant coherent sheaves on the nilpotent cone for complex reductive Lie groups, Ph.D. thesis, Massachusetts Institute of Technology, 2001. bezrukavnikov:tensor R. Bezrukavnikov, On tensor categories attached to cells in affine Weyl groups, arXiv:math.RT/0010089. bezrukavnikov:3 —, Perverse sheaves on affine flags and nilpotent cone of the Langlands dual group, arXiv:math.RT/0201073. bezrukavnikov:quasi-exc —, Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent cone, arXiv:math.RT/0102039. chm-ostrik:dist-inv T. Chmutova and V. Ostrik, Calculating distinguished involutions in the affine Weyl groups, arXiv:math.RT/0106011.
  • David H. Collingwood and William M. McGovern, Nilpotent orbits in semisimple Lie algebras, Van Nostrand Reinhold Mathematics Series, Van Nostrand Reinhold Co., New York, 1993. MR 1251060
  • Michel Demazure, A very simple proof of Bott’s theorem, Invent. Math. 33 (1976), no. 3, 271–272. MR 414569, DOI 10.1007/BF01404206
  • V. Hinich, On the singularities of nilpotent orbits, Israel J. Math. 73 (1991), no. 3, 297–308. MR 1135219, DOI 10.1007/BF02773843
  • George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
  • George Lusztig, Cells in affine Weyl groups. IV, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (1989), no. 2, 297–328. MR 1015001
  • G. Lusztig, Notes on unipotent classes, Asian J. Math. 1 (1997), no. 1, 194–207. MR 1480994, DOI 10.4310/AJM.1997.v1.n1.a7
  • William M. McGovern, Rings of regular functions on nilpotent orbits and their covers, Invent. Math. 97 (1989), no. 1, 209–217. MR 999319, DOI 10.1007/BF01850661
  • Viktor Ostrik, On the equivariant $K$-theory of the nilpotent cone, Represent. Theory 4 (2000), 296–305. MR 1773863, DOI 10.1090/S1088-4165-00-00089-3
  • D. I. Panyushev, Rationality of singularities and the Gorenstein property of nilpotent orbits, Funktsional. Anal. i Prilozhen. 25 (1991), no. 3, 76–78 (Russian); English transl., Funct. Anal. Appl. 25 (1991), no. 3, 225–226 (1992). MR 1139878, DOI 10.1007/BF01085494
  • Eric Sommers, Lusztig’s canonical quotient and generalized duality, J. Algebra 243 (2001), no. 2, 790–812. MR 1850659, DOI 10.1006/jabr.2001.8868
  • xi:xi N. Xi, The based ring of two-sided cells of affine Weyl groups of type $\widetilde A_ {n-1}$, Memoirs of the Amer. Math. Soc. 157 (2002), no. 749.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 17B10, 32L20
  • Retrieve articles in all journals with MSC (2000): 17B10, 32L20
Bibliographic Information
  • Pramod N. Achar
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • MR Author ID: 701892
  • Email:
  • Eric N. Sommers
  • Affiliation: Department of Mathematics, University of Massachusetts—Amherst, Amherst, Massachusetts 01003
  • Address at time of publication: School of Mathematics, IAS, Princeton, New Jersey 08540
  • Received by editor(s): December 14, 2001
  • Received by editor(s) in revised form: July 26, 2002
  • Published electronically: September 5, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Represent. Theory 6 (2002), 190-201
  • MSC (2000): Primary 17B10, 32L20
  • DOI:
  • MathSciNet review: 1927953