# Kazhdan-Lusztig left cells in type $B_n$ for intermediate parameters

## TL;DR

This paper verifies a conjecture about Kazhdan-Lusztig cells in type B_n Hecke algebras with intermediate parameters, using a generalized tau-invariant characterization.

## Contribution

It provides a proof confirming the conjectural description of Kazhdan-Lusztig cells in type B_n for intermediate parameters, advancing understanding in this algebraic area.

## Key findings

- Confirmed the conjectural description of Kazhdan-Lusztig cells in type B_n
- Utilized a generalized tau-invariant characterization
- Validated the structure for intermediate parameter Hecke algebras

## Abstract

Using a characterization of a generalized $\tau$-invariant for intermediate parameter Hecke algebras in type $B_n$, we verify a conjectural description of Kazhdan-Lusztig cells in this setting due to C. Bonnaf\'e, L. Iancu, M. Geck, and T. Lam.