# Nikolaus conference 2017

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.