Geodesic
An index formula for groups of isometric linear canonical transformations
Documenta mathematica, Tome 27 (2022), pp. 983-1013.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We define a representation of the unitary group $U(n)$ by metaplectic operators acting on $L^2(\mathbb{R}^n)$ 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.
Classification : 58J20, 58J40, 19K56
Keywords: index theory, Shubin class pseudodifferential operators ;metaplectic operators 
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Savin, Anton; Schrohe, Elmar. An index formula for groups of isometric linear canonical transformations. Documenta mathematica, Tome 27 (2022), pp. 983-1013. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a41/