## Proceedings of the International Conference on Geometry, Integrability and Quantization

### Analysis Over $C^*$-Algebras and the Oscillatory Representation

Svatopluk Krýsl

#### Abstract

Since the last two decades, several differential operators appeared in connection with the so-called oscillatory geometry. These operators act on sections of infinite rank vector bundles. Definitions of the oscillatory representation, metaplectic structure, oscillatory Dirac operator, as well as some necessary fundamental results in the analysis in $C^*$-Hilbert bundles are recalled here. These results are used for a description of the kernel of a certain second order differential operator arising from oscillatory geometry and the cohomology groups of the de Rham complex of exterior forms with values in the oscillatory representation.

#### Article information

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815710

Digital Object Identifier
doi:10.7546/giq-15-2014-173-195

Mathematical Reviews number (MathSciNet)
MR3222636

Zentralblatt MATH identifier
1321.81036

#### Citation

Krýsl, Svatopluk. Analysis Over $C^*$-Algebras and the Oscillatory Representation. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 173--195, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-173-195. https://projecteuclid.org/euclid.pgiq/1436815710