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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
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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.

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Additional Information

A. V. Smirnov
Affiliation: Moscow State University, Faculty of Mechanics and Mathematics, Moscow 119899, Russia

PII: S 0077-1554(04)00143-8
Posted: November 4, 2004
Article copyright: © Copyright 2004 American Mathematical Society