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

Abstract

We extend the work in a previous paper with David Li-Bland to construct the Wehrheim-Woodward category WW(𝐺SLREL) 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(SLREL) may be identified with pairs (𝐿, 𝑘) consisting of a linear canonical relation and a nonnegative integer.