The Maslov index as a quadratic space
Abstract
Kashiwara defined the Maslov index (associated to a collection of Lagrangian subspaces of a symplectic vector space over a field F) as a class in the Witt group W(F) of quadratic forms. We construct a canonical quadratic vector space in this class and show how to understand the basic properties of the Maslov index without passing to W(F)that is, more or less, how to upgrade Kashiwara's equalities in W(F) to canonical isomorphisms between quadratic spaces. We also show how our canonical quadratic form occurs naturally in the context of the Weil representation. The quadratic space is defined using elementary linear algebra. On the other hand, it has a nice interpretation in terms of sheaf cohomology, due to A. Beilinson.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2005
 DOI:
 10.48550/arXiv.math/0505561
 arXiv:
 arXiv:math/0505561
 Bibcode:
 2005math......5561T
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Representation Theory
 EPrint:
 20 pages, 2 figures. Presumably final version. The published version omits sections 911