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

2012/11/23 by Michèle Vergne, Vergne, Michèle
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1211.5547

openalex publication_date 2012/11/23 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

Let G be a connected compact Lie group acting on a manifold M and let D be a\ntransversally elliptic operator on M. The multiplicity of the index of D is a\nfunction on the set of irreducible representations of G. Let T be a maximal\ntorus of G with Lie algebra Lie(T). We construct a finite number of piecewise\npolynomial functions on the dual vector space Lie(T)*, and give a formula for\nthe multiplicity in term of these functions. The main new concept is the formal\nequivariant A class.\n

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