Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

Decomposition of symmetric powers of irreducible representations of semisimple Lie algebras and the Brion polytope


Author: A. V. Smirnov
Translated by: D. R. J. Chillingworth
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 65 (2004).
Journal: Trans. Moscow Math. Soc. 2004, 213-234
MSC (2000): Primary 20G05, 22E46, 53D20
Posted: November 4, 2004
MathSciNet review: 2193441
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: To any closed irreducible $G$-invariant cone in the space $V$ of a finite-dimensional representation of a semisimple Lie group there corresponds a convex polytope called the Brion polytope. This is closely connected with the action of the group $G$ on the algebra of functions on the cone, and also with the moment map. In this paper we give a description of Brion polytopes for the spaces $V$ themselves and for their nullcones.


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


Similar Articles

Retrieve articles in Transactions of the Moscow Mathematical Society with MSC (2000): 20G05, 22E46, 53D20

Retrieve articles in all journals with MSC (2000): 20G05, 22E46, 53D20


Additional Information

A. V. Smirnov
Affiliation: Moscow State University, Faculty of Mechanics and Mathematics, Moscow 119899, Russia
Email: asmirnov@rdm.ru

DOI: http://dx.doi.org/10.1090/S0077-1554-04-00143-8
PII: S 0077-1554(04)00143-8
Posted: November 4, 2004
Article copyright: © Copyright 2004 American Mathematical Society