JournalsprimsVol. 47, No. 1pp. 141–151

Asymptotic Equivariant Index of Toeplitz Operators on the Sphere

  • Louis Boutet de Monvel

    Université Pierre et Marie Curie, Paris, France
Asymptotic Equivariant Index of Toeplitz Operators on the Sphere cover

Abstract

We illustrate the equivariant asymptotic index described in [6, 8] in the case of spheres S2N1CN\mathbb{S}^{2N-1}\subset\mathbb{C}^N, equipped with a unitary action of a compact group, for which this theory is more explicit. The article is mostly a review article, except for the last section (§5) in which we describe conjecturally some very natural generators of the relevant K-theory for a torus action on a sphere, generalizing in our Toeplitz operator context the generators proposed by M. F. Atiyah [2] for the transversally elliptic pseudodi erential theory.

Cite this article

Louis Boutet de Monvel, Asymptotic Equivariant Index of Toeplitz Operators on the Sphere. Publ. Res. Inst. Math. Sci. 47 (2011), no. 1, pp. 141–151

DOI 10.2977/PRIMS/33