Formal equivariant (A)over-cap class, splines and multiplicities of the index of transversally elliptic operators

摘要

Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set (G) over cap of irreducible representations of G. Let T be a maximal torus of G with Lie algebra t. We construct a finite number of piecewise polynomial functions on t*, and give a formula for the multiplicity in terms of these functions. The main new concept is the formal equivariant (A) over cap class.