Constructible representations and basic sets in type B

TL;DR

This paper investigates the parametrization of simple modules in type B Weyl groups using basic sets, establishing their existence and the controlling role of constructible representation matrices.

Contribution

It demonstrates the existence of basic sets for matrices of constructible representations in type B and analyzes the bijections between different basic sets.

Findings

Basic sets exist for matrices of constructible representations in type B.

Bijections between basic sets are governed by constructible representation matrices.

The study advances understanding of module parametrizations in type B Weyl groups.

Abstract

We study the parametrizations of simple modules provided by the theory of basic sets for all finite Weyl groups. In the case of type B, we show the existence of basic sets for the matrices of constructible representations. Then we study bijections between the various basic sets and show that they are controlled by the matrices of the constructible representations.