The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups, which allows us to easily reproduce the cellularity of these algebras. This theorem generalizes a result of East about the cellularity of semigroup algebras of inverse semigroups.
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.
A complete mapping of a group G is a permutation φ : G → G such that g → gφ(g) is also a permutation. Complete mappings of G are equivalent to transversals of the Cayley table of G, considered as a Latin square. In 1953, Hall and Paige proved that a finite group admits a complete mapping only if its Sylow-2 subgroup is trivial or noncyclic. They conjectured that this condition is also sufficient. We prove that it is sufficient to check the conjecture for the 26 sporadic simple groups and the Tits group.
We first consider the rational Cherednik algebra corresponding to the action of a finite group on a complex variety, as defined by Etingof. We define a category of representations of this algebra which is analogous to "category O" for the rational Cherednik algebra of a vector space. We generalise to this setting Bezrukavnikov and Etingof's results about the possible support sets of such representations. Then we focus on the case of Sn acting on C n , determining which irreducible modules in this category have which support sets. We also show that the category of representations with a given support, modulo those with smaller support, is equivalent to the category of finite dimensional representations of a certain Hecke algebra.
Abstract. We introduce a new family of superalgebras, the quantum walled Brauer-Clifford superalgebras BCr,s(q). The superalgebra BCr,s(q) is a quantum deformation of the walled BrauerClifford superalgebra BCr,s and a super version of the quantum walled Brauer algebra. We prove that BCr,s(q) is the centralizer superalgebra of the action of Uq(q(n)) on the mixed tensor space V r,s q⊗s when n ≥ r + s, where Vq = C(q) (n|n) is the natural representation of the quantum enveloping superalgebra Uq(q(n)) and V * q is its dual space. We also provide a diagrammatic realization of BCr,s(q) as the (r, s)-bead tangle algebra BTr,s(q). Finally, we define the notion of q-Schur superalgebras of type Q and establish their basic properties.
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