By Stouffer E. B.

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6. J. J. Heckman: On the variation in the cohomology of the symplectic form of the reduced phase space. Invent. Math. 69 (1982), 259–268. 7. W. Guillemin, S. Sternberg: Convexity properties of the moment mapping. Invent. Math. 67 (1982), 491–513. 8. W. Guillemin, S. Sternberg: Geometric quantization and multiplicities of group representations. Invent. Math. 67 (1982), 515–538. 9. J. Heckman: Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups. Invent.

The orthogonal bundle T H M K to T X| M K in T M K is also T -invariant. 4. In particular the torus T now acts along the fibres of this projection. 2, the formulas of Duistermaat–Heckman are compatible to functorial operations. Given our choice of metrics, there are associated K currents ε M on M, ε S on S and ε M on M K . One can then ask to what extent these currents are compatible. Analogues of natural identities relating similar currents were established in [BGS90b]. 4, for > 0, it is natural to introduce the T -invariant metric g T M on T M given by 1 gT M = gT M + π ∗ gT S .

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