Core blocks of Ariki–Koike algebras

We examine blocks of the Ariki–Koike algebra, in an attempt to generalise the combinatorial representation theory of the Iwahori–Hecke algebra of type A. We identify a particular type of combinatorial block, which we call a core block, which may be viewed as an analogue of a simple block of the Iwahori–Hecke algebra. We give equivalent characterisations of core blocks and examine their basic combinatorics.     

Involutions of Iwahori–Hecke Algebras and Representations of Fixed Subalgebras

We establish branching rules between some Iwahori–Hecke algebra of type B and their subalgebras which are defined as fixed subalgebras by involutions including Goldman involution. The Iwahori–Hecke algebra of type D is one of such fixed subalgebras. We also obtain branching rules between those fixed subalgebras and their intersection subalgebra. We determine basic sets of irreducible representations of those fixed subalgebras and their intersection by making use of generalized Clifford theory.     

Explicit irreducible representations of the¶Iwahori–Hecke algebra of Type F4

A general method for computing irreducible representations of Weyl groups and Iwahori–Hecke algebras was introduced by the first author in [10]. In that paper the representations of the algebras of types A _n , B _n , D _n and G _n were computed and it is the purpose of this paper to extend these computations to F ₄. The main goal here is to compute irreducible representations of the Iwahori–Hecke algebra of type F ₄ by only using information in the character table of the Weyl group. Received: Received: 30 July 1998     

Subalgebra extensions of partial monounary algebras

For a subalgebra B of a partial monounary algebra A we define the quotient partial monounary algebra A/B. Let B, B, C be partial monounary algebras. In this paper we give a construction of all partial monounary algebras A such that B is a subalgebra of A and C ≅ A/B.     

L'algèbre de Lie des transpositions

For any n3 we obtain the decomposition in simple factors of the Lie subalgebra of the group algebra of the symmetric group on n letters generated by the transpositions. This enables us to determine the algebraic hull of the braid group B_n and of several of its subgroups inside the representations of the Iwahori–Hecke algebra of type A.     

Dirac cohomology of the Dunkl-Opdam subalgebra via inherited Drinfeld properties

Abstract

In this paper, we define a new presentation for the Dunkl-Opdam subalgebra of the rational Cherednik algebra. This presentation uncovers the Dunkl-Opdam subalgebra as a Drinfeld algebra. We use this fact to define Dirac cohomology for the DO subalgebra. We also formalize generalized graded Hecke algebras and extend a Langlands classification to generalized graded Hecke algebras.     

The Compact Quantum Group Uq（2） （Ⅱ）

In this paper, we first prove that the θ-deformation Uθ（2） of U（2） constructed by Connes and Violette is our special case of the quantum group Uq（2） constructed in our previous paper. Then we will show that the set of truces on the C^＊ -algebra Uθ, θ irrational, is determined by the set of the truces on a subalgebra of Uθ.     

The q-Analogue of the Alternating Group and Its Representations

We define the new algebra. This algebra has a parameter q. The defining relations of this algebra at q = 1 coincide with the basic relations of the alternating group. We also give the new subalgebra of the Hecke algebra of type A which is isomorphic to this algebra. This algebra is free of rank half that of the Hecke algebra. Hence this algebra is regarded as a q-analogue of the alternating group.All the isomorphism classes of the irreducible representations of this algebra and the q-analogue of the branching rule between the symmetric group and the alternating group are obtained.