Some remarks on combinatorial wall-crossing

TL;DR

This paper provides a new explicit description of combinatorial wall-crossing for the rational Cherednik algebra, recovering known results and proposing new conjectures based on computational experiments.

Contribution

It introduces a simplified explicit description of combinatorial wall-crossing and presents two new conjectures supported by computer experiments.

Findings

Recovered a theorem of Dimakis and Yue.

Proposed two new conjectures on combinatorial wall-crossing.

Established a new explicit description for the wall-crossing process.

Abstract

We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two conjectures on combinatorial wall-crossing which were found using computer experiments.