Symplectic quotients by a nonabelian group and by its maximal torus

By Shaun Martin. 2000

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G (0)/G, whereG : X → Lie(G) ∗ is a moment map for the G-action on X. A choice of maximal torus T ⊂ G induces a natural projection Lie(G) ∗ ։ Lie(T) ∗ , and composing withG gives a moment mapT : X → Lie(T) ∗ for the T-action, with X//T := � −1 T (0)/T. In most of this paper we make some additional simplifying assumptions: we assume that both � −1 G (0) and � −1 T (0) are compact manifolds, on which the respective G- and T-actions are free. It follows that X//G and X//T are compact symplectic manifolds. In section 6 we show how to modify the main results when various of these assumptions are dropped. For every weight α of T there is a characteristic class e(α) ∈ H 2 (X//T) naturally asso- ciated 1 to the principal T-bundle � −1

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/249597bbd0d5204b4cc6eec939dc4e94267843e3

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

The Abelian/Nonabelian correspondence and Frobenius manifolds (2006, background): “ Xs(G)/T →Xs(G)/G with ⊕α∈ΦLα|Xs(G)/T. In the nonequivariant case (that is, for S=1), (3.1.1) is a classical result, (3.1.2) is proved in [ES] for X = PN and in [Kir] in general, (3.1.3) is proved in [Mar] and (3.1.4) can be seen by a direct computation. The extensions to the equivariant context are”