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. [7]). 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 [1] which is in a sense universal for index computations.
Vector partition functions and index of transversally elliptic operators / DE CONCINI, Corrado; Procesi, Claudio; M., Vergne. - In: TRANSFORMATION GROUPS. - ISSN 1083-4362. - 15:4(2010), pp. 775-811. [10.1007/s00031-010-9101-x]
Vector partition functions and index of transversally elliptic operators
DE CONCINI, Corrado;PROCESI, Claudio;
2010
Abstract
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. [7]). 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 [1] which is in a sense universal for index computations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.