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Heat Kernels and Dirac Operators
The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recentExpand
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On the Segal-Shale-Weil representations and harmonic polynomials
In this paper, we give the answer to the following two intimately related problems. (a) To decompose the tensor products of the harmonic representations into irreducible components to get a series ofExpand
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Zeros d’un champ de vecteurs et classes caracteristiques equivariantes
Introduction, Soit M une variété différentiable, munie d'une action d'un groupe de Lie T. Soit t l'algèbre de Lie de T. Dans [2] nous avons introduit des espaces de cohomologie équivariante H(X),Expand
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Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes
© Bulletin de la S. M. F., 1970, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand
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Lattice points in simple polytopes
in terms of fP(h) q(x)dx where the polytope P(h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula ofExpand
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Kostant Partitions Functions and Flow Polytopes
This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The general approach that studies these functions via rational functions with poles on arrangement ofExpand
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Residue formulae, vector partition functions and lattice points in rational polytopes
We obtain residue formulae for certain functions of several vari- ables. As an application, we obtain closed formulae for vector partition func- tions and for their continuous analogs. They imply anExpand
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Modular forms of weight 1/2
We will construct θ-series of weight 1/2 and 3/2 for some congruence subgroups of SL(2,ℤ) by taking appropriate coefficients of the representation \( \mathop{R}\limits^{\sim } \) of SL(2;ℝ),Expand
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Local Euler-Maclaurin formula for polytopes
We give a local Euler-Maclaurin formula for rational convex polytopes in a rational euclidean space . For every affine rational polyhedral cone C in a rational euclidean space W, we construct aExpand
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