# Classification of the finite-dimensional unitary representations of type B rational Cherednik algebras

## TL;DR

This paper establishes a combinatorial classification of all finite-dimensional unitary irreducible representations of type B rational Cherednik algebras, linking crystal combinatorics with representation theory.

## Contribution

It provides a new proof that such representations are labeled by bipartitions with a rectangular partition and an empty partition, connecting crystal combinatorics to algebraic classification.

## Key findings

- Finite-dimensional unitary irreducible representations are labeled by bipartitions with a rectangular partition.
- The classification is achieved through crystal combinatorics of the level 2 Fock space.
- The result offers a new proof of existing theorems by Montarani and Etingof-Stoica.

## Abstract

We compare crystal combinatorics of the level $2$ Fock space with the classification of unitary representations of type $B$ rational Cherednik algebras to show that any finite-dimensional unitary irreducible representation of such an algebra is labeled by a bipartition consisting of a rectangular partition in one component and the empty partition in the other component. This is a new proof of a result that can be deduced from theorems of Montarani and Etingof-Stoica.