We define and study cyclotomic quotients of affine Hecke algebras of type B.
We establish an isomorphism between direct sums of blocks of these algebras and
a generalisation, for type B, of cyclotomic quiver Hecke algebras which are a
family of graded algebras closely related to algebras introduced by Varagnolo
and Vasserot. Inspired by the work of Brundan and Kleshchev we first give a
family of isomorphisms for the corresponding result in type A which includes
their original isomorphism. We then select a particular isomorphism from this
family and use it to prove our result.Comment: 37 page