Speaker: Johannes Hahn (Jena)
Title: Induction of W-Graphs
Abstract:
Let \(W\) be a finite Coxeter group and \(H\) its Iwahori-Hecke-algebra. \(W\)-graphs are a combinatorial way to encode matrix representations of \(H\), most prominently left Kazhdan-Lusztig cells give rise to \(W\)-graphs. Given a parabolic subalgebra \(H_J\) and a \(W_J\)-graph defining a \(H_J\)-module \(V\), Howlett and Yin gave an explicit construction how to obtain a \(W\)-graph for the induced representation \(Ind_{H_J}^H(V)\). In this talk an abstraction and generalisation of this procedure is given that is functorial in the appropriate sense, satisfies a transitivity statement and an analogue to Mackey's formula that generalises and makes more precise a simpler statement by Howlett and Yin.