Categorical actions of generalised braids for $n=3$
Abstract
Khovanov and Thomas constructed a categorical action of the braid group $Br_n$ on the derived category $D(T^* Fl_n)$ of coherent sheaves on the cotangent bundle of the variety $Fl_n$ of the complete flags in $\mathbb{C}^n$. In this paper, we define the generalised braid category $GBr_3$, give a sufficient condition for the existence of a skein-triangulated $GBr_3$ categorical action, and construct a categorical action of $GBr_3$ on $D(T^*(Fl_3(\bar{i}))$ that generalises Khovanov and Thomas categorical braid action on $D(T^* Fl_3)$.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.06115
- arXiv:
- arXiv:2211.06115
- Bibcode:
- 2022arXiv221106115D
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 27 pages, comments welcome!