English

An Index Formula for Groups of Isometric Linear Canonical Transformations

Operator Algebras 2020-08-04 v1 K-Theory and Homology Quantum Algebra

Abstract

We define a representation of the unitary group U(n)U(n) by metaplectic operators acting on L2(Rn)L^2(\mathbb{R}^n) and consider the operator algebra generated by the operators of the representation and pseudodifferential operators of Shubin class. Under suitable conditions, we prove the Fredholm property for elements in this algebra and obtain an index formula.

Keywords

Cite

@article{arxiv.2008.00734,
  title  = {An Index Formula for Groups of Isometric Linear Canonical Transformations},
  author = {Anton Savin and Elmar Schrohe},
  journal= {arXiv preprint arXiv:2008.00734},
  year   = {2020}
}
R2 v1 2026-06-23T17:35:45.026Z