Remote Access Transactions of the Moscow Mathematical Society

Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

 
 

 

Coisotropic representations of reductive groups


Author: I. V. Losev
Translated by: O. Khleborodova
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 66 (2005).
Journal: Trans. Moscow Math. Soc. 2005, 143-168
MSC (2000): Primary 20C15
DOI: https://doi.org/10.1090/S0077-1554-05-00152-4
Published electronically: November 16, 2005
MathSciNet review: 2193432
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A symplectic action $ G:X$ of an algebraic group $ S$ on a symplectic algebraic variety $ X$ is called coisotropic if a generic orbit of this action is a coisotropic submanifold of $ X$. In this article a classification of coisotropic symplectic linear actions $ G:V$ is given in the case where $ G$ is a reductive group.


References [Enhancements On Off] (What's this?)

  • 1. E. M. Andreev, È. B. Vinberg, and A. G. Èlašvili, Orbits of highest dimension of semisimple linear Lie groups, Funkcional. Anal. i Priložen. 1 (1967), no. 4, 3–7 (Russian). MR 0267040
  • 2. N. Bourbaki, Éléments de mathématique. Fasc. XXXVIII: Groupes et algèbres de Lie. Chapitre VII: Sous-algèbres de Cartan, éléments réguliers. Chapitre VIII: Algèbres de Lie semi-simples déployées, Actualités Scientifiques et Industrielles, No. 1364. Hermann, Paris, 1975 (French). MR 0453824
  • 3. E. M. Andreev, È. B. Vinberg, and A. G. Èlašvili, Orbits of highest dimension of semisimple linear Lie groups, Funkcional. Anal. i Priložen. 1 (1967), no. 4, 3–7 (Russian). MR 0267040
  • 4. È. B. Vinberg and A. L. Onishchik, \cyr Seminar po gruppam Li i algebraicheskim gruppam, 2nd ed., URSS, Moscow, 1995 (Russian, with Russian summary). MR 1403378
  • 5. È. B. Vinberg and V. L. Popov, Invariant theory, Algebraic geometry, 4 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, pp. 137–314, 315 (Russian). MR 1100485
  • 6. A. G. Èlašvili, Stationary subalgebras of points of general position for irreducible linear Lie groups, Funkcional. Anal. i Priložen. 6 (1972), no. 2, 65–78 (Russian). MR 0304555
  • 7. A. G. Èlašvili, Canonical form and stationary subalgebras of points in general position for simple linear Lie groups, Funkcional. Anal. i Priložen. 6 (1972), no. 1, 51–62 (Russian). MR 0304554
  • 8. Chal Benson and Gail Ratcliff, Rationality of the generalized binomial coefficients for a multiplicity free action, J. Austral. Math. Soc. Ser. A 68 (2000), no. 3, 387–410. MR 1753368
  • 9. V. G. Kac, Some remarks on nilpotent orbits. J. Algebra 64 (1980), 190-213. MR 0575790 (81i:17005)
  • 10. Andrew S. Leahy, A classification of multiplicity free representations, J. Lie Theory 8 (1998), no. 2, 367–391. MR 1650378

Similar Articles

Retrieve articles in Transactions of the Moscow Mathematical Society with MSC (2000): 20C15

Retrieve articles in all journals with MSC (2000): 20C15


Additional Information

I. V. Losev
Affiliation: 2nd Bagration Per. 19–706, Minsk 220037, Belarus
Email: ivanlosev@yandex.ru

DOI: https://doi.org/10.1090/S0077-1554-05-00152-4
Published electronically: November 16, 2005
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society