Nazarov [Naz96] introduced an infinite dimensional algebra, which he called the affine Wenzl algebra, in his study of the Brauer algebras. In this paper we study certain “cyclotomic quotients” of these algebras. We construct the irreducible representations of these algebras in the generic case and use this to show that these algebras are free of rank rn (2n−1)!! (when Ω is u-admissible). We next show that these algebras are cellular and give a labelling for the simple modules of the cyclotomic Nazarov-Wenzl algebras over an arbitrary field. In particular, this gives a construction of all of the finite dimensional irreducible modules of the affine Wenzl algebra.

In the representation theory of finite groups, it is useful to know which ordinary irreducible representations remain irreducible modulo a prime p. For the symmetric groups [Sfr ]n, this amounts to determining which Specht modules are irreducible over a field of characteristic p. Throughout this note we work in characteristic 2, and in this case we classify the irreducible Specht modules, thereby verifying the conjecture in [3, p. 97].

Recall that a partition is 2-regular if all of its non-zero parts are distinct; otherwise the partition is 2-singular. The irreducible Specht modules Sλ with λ a 2-regular partition were classified in [2]. Let λ′ denote the partition conjugate to λ. If Sλ is irreducible, then Sλ′ is irreducible, since Sλ′ is isomorphic to the dual of Sλ tensored with the sign representation. It turns out that if neither λ nor λ′ is 2-regular, then Sλ is irreducible only if λ = (2, 2).

In order to state our theorem, we let l(k), for an integer k, be the least non-negative integer such that k<2l(k).