Formal equivariant $\hat A$ class, splines and multiplicities of the index of transversally elliptic operators

Michèle Vergne

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arXiv · 1211.5547

Formal equivariant $\hat A$ class, splines and multiplicities of the index of transversally elliptic operators

Michèle Vergne

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Abstract

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 of irreducible representations of G. Let T be a maximal torus of G with Lie algebra Lie(T). We construct a finite number of piecewise polynomial functions on the dual vector space Lie(T)*, and give a formula for the multiplicity in term of these functions. The main new concept is the formal equivariant $\hat A$ class.

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BibTeX RIS

Michèle Vergne. 2012-11-23. Formal equivariant $\hat A$ class, splines and multiplicities of the index of transversally elliptic operators. https://arxiv.org/abs/1211.5547

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