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Decomposition of symmetric powers of irreducible representations of semisimple Lie algebras and the Brion polytope
Author(s):
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
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Abstract:
To any closed irreducible  -invariant cone in the space  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  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  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
Email:
asmirnov@rdm.ru
DOI:
10.1090/S0077-1554-04-00143-8
PII:
S 0077-1554(04)00143-8
Posted:
November 4, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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