Equivariant Dirac operators and differentiable geometric invariant theory

Paul-Emile Paradan (1, 2) , Michele Vergne (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 IMJ - Institut de Mathématiques de Jussieu

In this paper, we give a geometric expression for the multiplicities of the equivariant index of a spin-c Dirac operator.

Mots clés: Equivariant index; Multiplicity; Transversally elliptic symbol; Spin^c structures

Domaines: Géométrie différentielle [math.DG]; K-théorie et homologie [math.KT]; Géométrie symplectique [math.SG]

Paul-Emile Paradan, Michele Vergne. Equivariant Dirac operators and differentiable geometric invariant theory. Acta Mathematica, 2017, 218 (1), pp.137-199. ⟨10.4310/ACTA.2017.v218.n1.a3⟩. ⟨hal-01087892v3⟩