Introduction In this talk all groups are finite (by definition), and all simple groups are non-abelian. Let us first define our terms: an involution in a group G is an element t of order 2, i.e. t = 1 and t 6= 1. Its centralizer CG(t) is the subgroup of elements which commute with it, so CG(t) = {g ∈ G | tg = gt}. It has long been accepted in abstract group theory that the way to study simple g...

The purpose of this paper is to investigate the finite group which appears in the study of the Type II Z4-codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer algebras of the tensor representations of this group.

We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space ∆ ⊗⊗ k V . Here ∆ is the fundamental representation of Pin(N) and V is the natural (vector) representation of the orthogonal group O(N). We consider the centralizer algebra CPk = EndPin(N)(∆ ⊗⊗k V ) for Pin(N), the double covering group of O(N) and define...

A modular theory for permutation representations and their centralizer rings is presented, analogous in several respects to the classical work of Brauer on group algebras. Some principal ingredients of the theory are characters of indecomposable components of the permutation module over a p-adic ring, modular characters of the centralizer ring, and the action of normalizers of p-subgroups P on ...

Generically (for r + s ≥ n) the centralizer algebra for the action of GLn(C) on mixed tensor space (C n) ⊗r ⊗ ((C n) *) ⊗s is a certain subalgebra of the Brauer algebra, known as the walled (or rational) Brauer algebra. This paper studies a q-deformation, B n r,s (q), of the walled Brauer algebra and shows that the centralizer algebra for the action of the quantum group UR(gl n) on mixed tensor...

In this paper we study some combinatorial aspects of the singular Artin monoids. Firstly, we show that a singular Artin monoid SA can be presented as a semidirect product of a graph monoid with its associated Artin group A. Such a decomposition implies that a singular Artin monoid embeds in a group. Secondly, we give a solution to the word problem for the FC type singular Artin monoids. Afterwa...

Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan