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

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.