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BGG Resolutions, Koszulity, and Stratifications, Part I: the nilBrauer Algebra
Fan Zhou
https://arxiv.org/abs/2402.06890 https://arxi…

BGG Resolutions, Koszulity, and Stratifications, Part I: the nilBrauer Algebra
In this paper we homologically construct a (functorial) BGG resolution of the finite-dimensional simple module of the nilBrauer algebra by using infinity-categorical methods following the reconstruction-from-stratification philosophy, e.g. appearing in Ayala-Mazel-Gee-Rozenblyum. To do so, we prove a fact of independent interest, that half of the nilBrauer algebra is Koszul. This BGG resolution categorifies a character formula of Brundan-Wang-Webster. More generally, we have a (functorial) ``BG…