The spin Brauer category
Abstract
We introduce a diagrammatic monoidal category, the spin Brauer category, that plays the same role for the spin and pin groups as the Brauer category does for the orthogonal groups. In particular, there is a full functor from the spin Brauer category to the category of finite-dimensional modules for the spin and pin groups. This functor becomes essentially surjective after passing to the Karoubi envelope, and its kernel is the tensor ideal of negligible morphisms. In this way, the spin Brauer category can be thought of as an interpolating category for the spin and pin groups. We also define an affine version of the spin Brauer category, which acts on categories of modules for the pin and spin groups via translation functors.
Cite
@article{arxiv.2312.11766,
title = {The spin Brauer category},
author = {Peter J. McNamara and Alistair Savage},
journal= {arXiv preprint arXiv:2312.11766},
year = {2025}
}
Comments
46 pages. v2: Changed order of Sections 7 and 8, other improvements and corrections throughout. v3: Footnote added pointing out a gap in the proof of a theorem and how to fix it