Relative Serre duality for Coxeter groups

Abstract

It was conjectured by Gorsky, Hogancamp, Mellit, and Nakagane that the left and right adjoints of the parabolic induction functor between homotopy categories of Soergel bimodules associated to a finite Coxeter group are related by the relative full twist. Several cases of this conjecture are known including for symmetric groups, crystallographic Coxeter groups, and dihedral groups. We prove this conjecture in complete generality using the theory of Abe-Bott-Samelson bimodules and the Achar-Riche-Vay mixed derived category.