Lusztig $\mathbf{a}$-functions for quasiparabolic sets
Lusztig $\mathbf{a}$-functions for quasiparabolic sets
Kazhdan and Lusztig introduce the $W$-graphs to describe the cells and molecules corresponding to the Coxeter groups. Building on this foundation, Lusztig defines the a-funtion to classify the cells, as well as the molecules. Marberg then generalizes Kazhdan and Lusztig's $W$-graphs, using fixed-point-free involutions as their indices. The molecules of …