The Soergel category and the redotted Webster algebra

A braid group action on a $p$-DG homotopy category

“…We show that there are braiding complexes in a homotopy category of p-DG W -modules using key ideas from [KR16]. Using some results from p-DG theory we extend the main result of [KS18] to the p-DG setting.…”

“…We begin by recalling the definition of a particular deformed Webster algebra W (n, 1). More general versions of these algebras W (s, n) can be found in [KS18,KLSY18]. The p-DG structures on these algebras were introduced in [Yon].…”

“…A basis for the cyclotomic deformed Webster W (n, 1) was given in [KS18] (see also [Web] and [SW11]). We slightly modify this basis and a representation of the algebra for the case where the cyclotomic condition is omitted.…”

“…. , n − 1 was introduced in [KS18]. We consider collections of smooth arcs in the plane connecting n red points and 1 black point on one horizontal line with n red points and 1 black point on another horizontal line.…”

“…Partially motivated by the construction in [QS16], a deformation W = W (n, 1) of A ! n was considered in [KS18] and the authors showed that there is a categorical braid group action on the homotopy category of W -modules. This result was extended in [KLSY18] to a categorical braid group action on the homotopy category of a deformation of more general Webster algebras for sl 2 , for which W is a special case (hence the notation).…”