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Jeffrey and Kirwan gave expressions for intersection pairings on the reduced space of a Hamiltonian space in terms of iterated residues. Alekseev, Malkin, and Meinrenken introduced the notion of quasi-Hamiltonian spaces for which the moment map takes values in the group itself rather than in the dual of the Lie algebra, and developed the theory of quasi-Hamiltonian spaces. The theory includes counterparts of Hamiltonian reductions. Alekseev, Meinrenken, and Woodward proved a localization formula for group valued equivariant de Rham cohomology of a compact G-manifold. From this result a Duistermaat-Heckman formula for group valued moment maps was derived.In this paper, we construct the Hamiltonian space corresponding to a given quasi-Hamiltonian space. We use an important property of the Hamiltonian spaces: periodicity. We first prove a residue formula for intersection numbers in the reduced space of a quasi-Hamiltonian T-space (where T is a compact torus) by induction on r, the rank of T. From that result, we prove a residue formula for intersection pairings of the reduced spaces of a quasi-Hamiltonian G-space (where G is a compact Lie group). We show that the result agrees with that in Alekseev-Meinrenken-Woodward. We rely heavily on the method of Jeffrey and Kirwan (Intersection theory on moduli spaces, which is the reduced space of the quasi-Hamiltonian SU(n)-space SU(n)2g). For the more general class of compact Lie group, we make use of the result on diagonal bases given by Szenes and Brion-Vergne.
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In this paper we prove a residue formula for intersection pairings of reduced spaces of certain quasi-Hamiltonian G-spaces, by constructing the corresponding Hamiltonian :// Witten's Nonabelian Localization for Noncompact Hamiltonian Spaces Article in Differential Geometry and its Applications 25(2) April with 20 Reads How we measure 'reads''s_Nonabelian_Localization. 第七届华人数学家大会会议安排手册_理学_高等教育_教育专区 79人阅读|次下载 第七届华人数学家大会会议安排手册_理学_高等教育_教育专区。 Contents Congress Chairman?:// Also, the genus expansion of the logarithm of the Witten - Kontsevich tau-function of KdV coincides with the generating function of the intersection numbers of certain cycles on the Deligne - Mumford moduli spaces of stable algebraic Web view.
Thesis title: Volume Formula and Intersection Pairings of N-fold Reduced Products Let $ G $ be a semisimple compact connected Lie group. An $ N $-fold reduced product of $ G $ is the symplectic quotient of the Hamiltonian system of the Cartesian product of $ N $ coadjoint orbits of $ G $ under diagonal coadjoint action of $ G $ Quasi-Hamiltonian spaces, introduced by Alekseev, Malkin, and Meinrenken, are similar to Hamiltonian G-manifolds but with two significant differences: first, the 2-form on the manifold is neither closed nor nondegenerate, but one has control over the image of the differential of the 2-form, as well as the degeneracy locus of the 2-form, and The collection of mean values in the Mean value theorem. reference-request real-analysis measure-theory mean-value-theorem. modified 12 mins ago OOESCoupling 1, Regularity of conformal maps. ential-geometry is-of-pdes x-variables riemannian-geometry conformal-geometry. modified 29 mins ago seub 1, Here, is the equivariant Cartan 3-form determined by an invariant inner product on the Lie algebra .The condition that ω be nondegenerate is replaced by the weaker condition that everywhere. Products, conjugates, and reductions are defined similar to the Hamiltonian case. Basic examples of q-Hamiltonian spaces are conjugacy classes , with moment map being the ://
GROUP LATTICES AND HOMOMORPHISMS D. NUCLEAR STATES In the shell model of the nucleus, the individual nucleons are assumed to move in a spherically symmetrical average Euclidean field described by a three-dimensional harmonic oscillator Hamiltonian The equation is separable into three one-dimensional harmonic oscillators with the same force MBA智库文档，专业的管理资源分享平台。分享管理资源，传递管理智慧。 Mathematical Tools for Data Mining Set Theory, Partial Orders, The symmetric energy-momentum tensor. It is a widely accepted view (appearing e.g. in excellent, standard textbooks on general relativity, too) that the canonical energy-momentum and spin tensors are well-defined and have relevance only in flat spacetime, and hence usually are underestimated and abandoned. However, it is only the analog of these canonical quantities that can be associated D. Agostinelli; R. Cerbino; J.C. Del Alamo; A. DeSimone; S. Höhn; C. Micheletti; G. Noselli; E. Sharon; J. Yeomans,?f[author]=