# Monodromy in Kazhdan-Lusztig cells in affine type A

## TL;DR

This paper explores the structure of Kazhdan-Lusztig cells in affine type A using the affine Robinson-Schensted correspondence, providing a detailed description of the related combinatorial objects and their equivalence classes.

## Contribution

It offers a comprehensive description of bidirected edges in Kazhdan-Lusztig cells and classifies Knuth equivalence classes of affine permutations in affine type A.

## Key findings

- Characterization of bidirected edges in Kazhdan-Lusztig cells
- Description of Knuth equivalence classes of affine permutations
- Application of affine Robinson-Schensted correspondence

## Abstract

We use the affine Robinson-Schensted correspondence to describe the structure of bidirected edges in the Kazhdan-Lusztig cells in affine type A. Equivalently, we give a comprehensive description of the Knuth equivalence classes of affine permutations.