Decomposition of symmetric powers of irreducible representations of semisimple Lie algebras and the Brion polytope
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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.References
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Bibliographic Information
- A. V. Smirnov
- Affiliation: Moscow State University, Faculty of Mechanics and Mathematics, Moscow 119899, Russia
- Email: asmirnov@rdm.ru
- Published electronically: November 4, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2004, 213-234
- MSC (2000): Primary 20G05, 22E46, 53D20
- DOI: https://doi.org/10.1090/S0077-1554-04-00143-8
- MathSciNet review: 2193441