Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group

TL;DR

This paper explores the relationship between canonical left cells and the lowest two-sided cell in an affine Weyl group, constructing modules and representations associated with these structures.

Contribution

It introduces a new approach to relate canonical left cells with the lowest two-sided cell and constructs related irreducible modules and one-dimensional representations.

Findings

Established relations between canonical left cells and the lowest two-sided cell

Constructed irreducible modules attached to the lowest two-sided cell

Developed one-dimensional representations of an affine Hecke algebra

Abstract

We give some discussions to the relations between canonical left cells and the lowest two-sided cell of an affine Weyl group. In particular, we use the relations to construct irreducible modules attached to the lowest two-sided cell and some one dimensional representations of an affine Hecke algebra.