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

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