Categorical actions of generalised braids for n=3

2022/11/11 by De Biase, Lorenzo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.06115

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 ℂⁿ. In this paper, we define the generalised braid category GBr₃, give a sufficient condition for the existence of a skein-triangulated GBr₃ categorical action, and construct a categorical action of GBr₃ on D(T^*(Fl₃(i)) that generalises Khovanov and Thomas categorical braid action on D(T^* Fl₃).

Related

• Braid group actions on derived categories of coherent sheaves
• Affine braid group actions on derived categories of Springer resolutions
• Braid Group Action on D^b(\mathfrakM_η)
• A remark on braid group actions on coherent sheaves
• Categorification of the braid groups