The nil-Brauer category (Q6580060)

The present authors introduce the nil-Brauer category and prove a basis theorem for its morphism spaces. This basis theorem is an essential ingredient required to prove that nil-Brauer categorifies the split \(\iota\)-quantum group of rank one. As this \(\iota\)-quantum group is a basic building block for \(\iota\)-quantum groups of higher rank, the authors expect that the nil-Brauer category will play a central role in future developments related to the categorification of quantum symmetric pairs. The main theorem about nil-Brauer category \(\mathcal{NB}_t\) gives explicit bases for morphism spaces in \(\mathcal{NB}_t\). Their proof follows a similar strategy to the approach developed for Khovanov's Heisenberg category, exploiting a certain monoidal functor obtained by localizing the \(2\)-category \(\mathfrak{U}(\mathfrak{sl}_2)\) at certain morphisms.