The nil-Brauer category is a (non-symmetric) \k-linear monoidal category which is a nil version of the affine Brauer category in the same way that the nil-Hecke algebra is a nil version of the affine Hecke algebra of GL_n. It is defined by innocuous-looking generators and relations. Our main theorem is that it categorifies the split \iota-quantum group of rank one in the sense of Letzter, Kolb and Bao--Wang. I also hope to explain two places that the nil-Brauer category arises "in nature", one involving the Lauda-Rouquier categorification of sl_2, and the other which relates it to singular Soergel bimodules associated to maximally isotropic Grassmannians in type D. This talk is based on joint works with Weiqiang Wang, Ben Webster, Elijah Bodish and Ben Elias.
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