Edge Transport from Parabolic Subgroups of Type $D_4$

TL;DR

This paper advances the classification of Kazhdan-Lusztig cells in Weyl groups of type D by analyzing edge transport related to a specific parabolic subgroup, contributing to the understanding of the generalized tau-invariant.

Contribution

It provides new results on Kazhdan-Lusztig cells for a type D_4 parabolic subgroup, extending previous classifications and applications to the tau-invariant.

Findings

Established analogous results to Kazhdan-Lusztig's original work for D_4

Connected edge transport to the definition of the generalized tau-invariant

Enhanced understanding of cell structures in Weyl groups of type D

Abstract

This paper is part of the program to classify Kazhdan-Lusztig cells for Weyl groups of type $D_n$. We prove analogous results to those of section 4 of Kazhdan-Lusztig's original paper, this time related to a parabolic subgroup of type $D_4$. We also show how this is used in the definition of the generalized $\tau$-invariant.