Crystal isomorphisms and wall-crossing maps for rational Cherednik algebras

TL;DR

This paper demonstrates that wall-crossing bijections in rational Cherednik algebras correspond to crystal isomorphisms, which can be computed through a straightforward combinatorial method on multipartitions.

Contribution

It establishes a direct link between wall-crossing bijections and crystal isomorphisms, providing a simple combinatorial approach for their computation.

Findings

Wall-crossing bijections reduce to crystal isomorphisms.

A simple combinatorial procedure for computing these isomorphisms.

The method applies to multipartitions of fixed rank.

Abstract

We show that the wall crossing bijections between simples of the category O of the rational Cherednik algebras reduce to particular crystal isomorphisms which can be computed by a simple combinatorial procedure on multipartitions of fixed rank.