The Wehrheim-Woodward Category of Linear Canonical Relations between $G$-Spaces

TL;DR

This paper generalizes the Wehrheim-Woodward category to include equivariant linear canonical relations between symplectic G-spaces, extending previous non-equivariant results and providing a categorical framework for symplectic G-space relations.

Contribution

It constructs the Wehrheim-Woodward category for equivariant linear canonical relations between symplectic G-spaces, extending prior work to the equivariant setting.

Findings

The category WW(GSLREL) includes morphisms as pairs of relations and integers.

When G is trivial, the category reduces to known non-equivariant results.

Provides a categorical structure for equivariant symplectic relations.

Abstract

We extend the work in a previous paper with David Li-Bland (arXiv:1401.7302) to construct the Wehrheim-Woodward category WW($G\mathbf{SLREL}$) of equivariant linear canonical relations between linear symplectic $G$-spaces for a compact group $G$. When $G$ is the trivial group, this reduces to the previous result that the morphisms in WW($\mathbf{SLREL}$) may be identified with pairs $(L,k)$ consisting of a linear canonical relation and a nonnegative integer.