Multiplication by $$T_{w_0}$$Tw0

Abstract

This chapter explains how the multiplication by \(T_{w_{0}}\) (where \({w_{0}}\) is the longest element of a finite Coxeter group) acts on Kazhdan–Lusztig basis elements: in particular, we show that it induces a non-trivial left (or right) cellular map, even if \({w_{0}}\) is central.