A remark on the moment map

Azad, H.

doi:10.1090/S0002-9939-1994-1191865-4

A remark on the moment map
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by H. Azad

Proc. Amer. Math. Soc. 121 (1994), 1295-1297

DOI: https://doi.org/10.1090/S0002-9939-1994-1191865-4

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Abstract:

Following S. Lie, it is proposed that moment maps be constructed for degenerate forms and the utility of such maps is illustrated by computing the moment maps for torus actions on ${{\mathbf {C}}^n}$ and $U(n)$ actions on ${{\mathbf {P}}^n}({\mathbf {C}})$.

References

Ralph Abraham and Jerrold E. Marsden, Foundations of mechanics, Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass., 1978. Second edition, revised and enlarged; With the assistance of Tudor Raţiu and Richard Cushman. MR 515141
A. M. Bloch and T. S. Ratiu, Convexity and integrability, Symplectic geometry and mathematical physics (Aix-en-Provence, 1990) Progr. Math., vol. 99, Birkhäuser Boston, Boston, MA, 1991, pp. 48–79. MR 1156534
V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), no. 3, 515–538. MR 664118, DOI 10.1007/BF01398934
Patrick Iglésias, Les $\textrm {SO}(3)$-variétés symplectiques et leur classification en dimension $4$, Bull. Soc. Math. France 119 (1991), no. 3, 371–396 (French, with English summary). MR 1125672
Frances Clare Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol. 31, Princeton University Press, Princeton, NJ, 1984. MR 766741, DOI 10.2307/j.ctv10vm2m8
Linda Ness, A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984), no. 6, 1281–1329. With an appendix by David Mumford. MR 765581, DOI 10.2307/2374395
J.-M. Souriau, Structure des systèmes dynamiques, Dunod, Paris, 1970 (French). Maîtrises de mathématiques. MR 0260238
Alan Weinstein, Sophus Lie and symplectic geometry, Exposition. Math. 1 (1983), no. 1, 95–96. MR 693812