Skip Navigation


Bulletin of the London Mathematical Society Advance Access originally published online on November 13, 2008
Bulletin of the London Mathematical Society 2008 40(6):1045-1064; doi:10.1112/blms/bdn090
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
40/6/1045    most recent
bdn090v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Panyushev, D. I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Adjoint vector fields and differential operators on representation spaces

Dmitri I. Panyushev

Institute for Information Transmission Problems
B. Karetnyi per. 19
Moscow 101447
and
Independent University of Moscow
Bol'shoi Vlasevskii per. 11
119002 Moscow
Russia
http://www.mccme.ru/~panyush

Received 25 February 2008. Revision received 9 July 2008.

Let G be a semisimple algebraic group with Lie algebra g. In 1979, J. Dixmier proved that any vector field annihilating all G-invariant polynomials on g lies in the Formula module generated by the ‘adjoint vector fields’, that is, vector fields {varsigma} of the form {varsigma}(y)(x) = [x, y], x, y isin g. A substantial generalisation of Dixmier's theorem was found by Levasseur and Stafford. They explicitly described the centraliser of Formula G in the algebra of differential operators on g. On the level of vector fields, their result reduces to Dixmier's theorem. The purpose of this paper is to explore similar problems in the general context of affine algebraic groups and their rational representations.

2000 Mathematics Subject Classification 14L30, 16S32, 17B20, 22E47.

Research supported in part by R.F.B.R. grant 06-01-72550.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.