On invariant operations of Fedosov structures

TL;DR

This paper investigates invariant local tensor operations on Fedosov manifolds, characterizing the space of natural tensors as finite-dimensional symplectic group representations, advancing understanding of geometric invariants.

Contribution

It provides a classification of homogeneous natural tensors on Fedosov manifolds using symplectic group representation theory, a novel approach in this context.

Findings

Spaces of natural tensors are finite-dimensional symplectic group representations

Classification of invariant tensor operations on Fedosov manifolds

Enhanced understanding of geometric invariants in symplectic geometry

Abstract

In this paper we study invariant local operations that can performed on a Fedosov manifold, with a particular emphasis on tensor-valued operations (also known as natural tensors). Our main result describes the spaces of homogeneous natural tensors as certain finite dimensional linear representations of the symplectic group.