A Note On The Representations Of Cyclotomic Nazarov-Wenzl Algebras

Suppose that R is a commutative ring with identity 1 and invertible element 2. In [2], Ariki, Mathas and Rui introduced a finite dimensional algebra W_m,n(u), called a cyclotomic Nazarov-Wenzl algebra. It is an associative algebra over R, with parameters Ω = {ω_a ∈ R | a ≥ 0} and u = (u₁,··· , u_m) ∈ R^m. When Ω is u—admissible (see ( 2.6)), Ariki, Mathas and Rui proved that W_m,n(u) is a cellular algebra over R with R-rank mⁿ ? (2n-1)!!. Suppose that R is a field containing the non-zero element ω₀. Ariki, Mathas and Rui classified the irreducible modules for W_m,n(u).This main purpose of this paper is to classify the irreducible modules for W_m,n(u) in general case. This gives a complete solution on the problem.