Abstract. The cyclotomic Birman-Murakami-Wenzl (or BMW) algebras B k n , introduced by R. Häring-Oldenburg, are extensions of the cyclotomic Hecke algebras of Ariki-Koike, in the same way as the BMW algebras are extensions of the Hecke algebras of type A. In this paper we focus on the case n = 2, producing a basis of B k 2 and constructing its left regular representation.
For each n ≥ 2, we define an algebra satisfying many properties that one might expect to hold for a Brauer algebra of type C n . The monomials of this algebra correspond to scalar multiples of symmetric Brauer diagrams on 2n strands. The algebra is shown to be free of rank the number of such diagrams and cellular, in the sense of Graham and Lehrer.
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