منابع مشابه
Cyclotomic Solomon Algebras
This paper introduces an analogue of the Solomon descent algebra for the complex reflection groups of type G(r, 1, n). As with the Solomon descent algebra, our algebra has a basis given by sums of ‘distinguished’ coset representatives for certain ‘reflection subgroups’. We explicitly describe the structure constants with respect to this basis and show that they are polynomials in r. This allows...
متن کاملCyclotomic Wenzl Algebras
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 r(2n − 1)!! (when Ω is u– admissible). We ne...
متن کاملCyclotomic Nazarov–wenzl Algebras
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 r(2n − 1)!! (when Ω is u–admissible). We nex...
متن کاملSymmetric Cyclotomic Hecke Algebras
In this paper we prove that the generic cyclotomic Hecke algebras for imprimitive complex reeection groups are symmetric over any ring containing inverses of the parameters. For this we show that the determinant of the Gram matrix of a certain canonical sym-metrizing form introduced in 3] is a unit in any such ring. On the way we show that the Ariki-Koike bases of these algebras are also quasi-...
متن کاملPresenting cyclotomic q-Schur algebras
We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras. § 0. Introduction Let Hn,r be an Ariki-Koike algebra associated to a complex reflection group Sn ⋉ (Z/rZ). A cyclotomic q-Schur algebra Sn,r associated to Hn,r, introduced in [DJM], is defined as a...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.05.009