Publications of the Research Institute for Mathematical Sciences

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Volume 47, Issue 1, 2011, pp. 141–151
DOI: 10.2977/PRIMS/33

Published online: 2011-03-24

Asymptotic Equivariant Index of Toeplitz Operators on the Sphere

Louis Boutet de Monvel

We illustrate the equivariant asymptotic index described in [6, 8] in the case of spheres $\mathbb{S}^{2N-1}\subset\mathbb{C}^N$, 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 (ยง5) 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.

Keywords: Toeplitz operators, index, equivariant K-theory, contact manifolds

Boutet de Monvel Louis: Asymptotic Equivariant Index of Toeplitz Operators on the Sphere. Publ. Res. Inst. Math. Sci. 47 (2011), 141-151. doi: 10.2977/PRIMS/33