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

Smirnov, A.

doi:10.1090/S0077-1554-04-00143-8

Decomposition of symmetric powers of irreducible representations of semisimple Lie algebras and the Brion polytope
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by A. V. Smirnov
Translated by: D. R. J. Chillingworth

Trans. Moscow Math. Soc. 2004, 213-234

DOI: https://doi.org/10.1090/S0077-1554-04-00143-8

Published electronically: November 4, 2004

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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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