We define an enhanced Brauer category $/wt/CB(m)$ by adding a single generator to the usual Brauer category $/CB(m)$, together with four relations. We then prove that our category $/wt/CB(m)$ is actually equivalent to the category of representations of $/SO_m$ generated by the natural representation. The FFT for $/SO_m$ amounts to the surjectivity of a certain functor $/CF$ on $/Hom$ spaces, while the Second Fundamental Theorem for $/SO_m$ says simply that $/CF$ is injective on $/Hom$ spaces. This theorem provides a diagrammatic means of computing the dimensions of spaces of homomorphisms between tensor modules for $/SO_m$. This is joint work with Gus Lehrer.

海报