Knop F (2006)
Publication Language: English
Publication Status: Published
Publication Type: Journal article, Original article
Publication year: 2006
Publisher: Elsevier
Book Volume: 301
Pages Range: 531-553
Journal Issue: 2
DOI: 10.1016/j.jalgebra.2005.07.035
Let G be a connected reductive group acting on a finite-dimensional vector space V. Assume that V is equipped with a G-invariant symplectic form. Then the ring O(V) of polynomial functions becomes a Poisson algebra. The ring O(V)(G) of invariants is a sub-Poisson algebra. We call V multiplicity free if O(V)(G) is Poisson commutative, i.e., if {f, g} = 0 for all invariants f and g. Alternatively, G also acts on the Weyl algebra W(V) and V is multiplicity free if and only if the subalgebra W(V)(G) of invariants is commutative. In this paper we classify all multiplicity free symplectic representations. (c) 2005 Elsevier Inc. All rights reserved.
APA:
Knop, F. (2006). Classification of multiplicity free symplectic representations. Journal of Algebra, 301(2), 531-553. https://dx.doi.org/10.1016/j.jalgebra.2005.07.035
MLA:
Knop, Friedrich. "Classification of multiplicity free symplectic representations." Journal of Algebra 301.2 (2006): 531-553.
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