Classification of multiplicity free symplectic representations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2005
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| _version_ | 1866916223230410752 |
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| author | Knop, Friedrich |
| author_facet | Knop, Friedrich |
| contents | 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 C[V] of polynomial functions becomes a Poisson algebra. The ring C[V]^G of invariants is a sub-Poisson algebra. We call V multiplicity free if C[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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0505268 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | Classification of multiplicity free symplectic representations Knop, Friedrich Symplectic Geometry Algebraic Geometry Representation Theory 53D20, 14L30, 22E46 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 C[V] of polynomial functions becomes a Poisson algebra. The ring C[V]^G of invariants is a sub-Poisson algebra. We call V multiplicity free if C[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. |
| title | Classification of multiplicity free symplectic representations |
| topic | Symplectic Geometry Algebraic Geometry Representation Theory 53D20, 14L30, 22E46 |
| url | https://arxiv.org/abs/math/0505268 |