Let G be a torus acting linearly on a complex vector space M and let X be the list of weights of G in M. We determine the topological equivariant K-theory of the open subset M-f of M consisting of points with finite stabilizers. We identify it to the space DM (X) of functions on the character lattice (G) over cap, satisfying the cocircuit difference equations associated to X, introduced by Dahmen and Micchelli in the context of the theory of splines in order to study vector partition functions (cf. ). This allows us to determine the range of the index map from G-transversally elliptic operators on M to generalized functions on G and to prove that the index map is an isomorphism on the image. This is a setting studied by Atiyah and Singer  which is in a sense universal for index computations.
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|Titolo:||Vector partition functions and index of transversally elliptic operators|
|Data di pubblicazione:||2010|
|Appartiene alla tipologia:||01a Articolo in rivista|