Cells and Constructible Representations in type B

TL;DR

This paper investigates the partition of type B Coxeter groups into cells based on a weight function, aiming to reconcile Lusztig's constructible representations with combinatorial cell descriptions.

Contribution

It provides a connection between Lusztig's constructible representations and combinatorial descriptions of cells in type B Coxeter groups.

Findings

Reconciliation of Lusztig's constructible representations with combinatorial cell descriptions.

Enhanced understanding of cell structure in type B Coxeter groups.

Clarification of the relationship between algebraic and combinatorial approaches.

Abstract

We examine the partition of a finite Coxeter group of type $B$ into cells determined by a weight function $L$. The main objective of these notes is to reconcile Lusztig's description of constructible representations in this setting with conjectured combinatorial descriptions of cells.