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Localization of the Riemann–Roch Character
Abstract We present a K-theoretic approach to the Guillemin–Sternberg conjecture (V. Guillemin and S. Sternberg, Invent. Math. 67 (1982), 515–538), about the commutativity of geometric quantizationExpand
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Spinc-quantization and the K-multiplicities of the discrete series
Abstract In the 70s, W. Schmid has shown that the representations of the discrete series of a real semi-simple Lie group G could be realized as the quantization of elliptic coadjoint orbits. In thisExpand
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The multiplicities of the equivariant index of twisted Dirac operators
In this note, we give a geometric expression for the multiplicities of the equivariant index of a Dirac operator twisted by a line bundle.
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The moment map and equivariant cohomology with generalized coefficients
Abstract Let M be a symplectic manifold acted on by a compact Lie group G in a Hamiltonian fashion, with proper moment map. In this situation we introduce a pushforward morphism P : H ∗ G (M)→ M −∞ (Expand
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Multiplicities of the discrete series
The purpose of this paper is to show that the multiplicities of a discrete series representation relatively to a compact subgroup can be ``computed'' geometrically, in the way predicted by theExpand
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Formal geometric quantization II
In this paper we pursue the study of formal geometric quantization of non-compact Hamiltonian manifolds. Our main result is the proof that two quantization process coincide. This fact was obtained byExpand
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Index of transversally elliptic operators
In 1996, Berline and Vergne gave a cohomological formula for the index of a transversally elliptic operator. In this paper we propose a new point of view where the cohomological formulae make use ofExpand
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Jump formulas in Hamiltonian Geometry
This paper is concerned with the Hamiltonian actions of a torus on a symplectic manifold. We are interested here in two global invariants: the Duistermaat-Heckman measure DH(M), and the Riemann-RochExpand
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Witten non abelian localization for equivariant K-theory, and the [Q,R]=0 theorem
The purpose of the present paper is two-fold. First, we obtain a non-abelian localization theorem when M is any even dimensional compact manifold : following an idea of E. Witten, we deform anExpand
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Equivariant relative Thom forms and Chern characters
These notes are the first chapter of a monograph, dedicated to a detailed proof of the equivariant index theorem for transversally elliptic operators. In this preliminary chapter, we prove a certainExpand
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