Let G be the adjoint group of a simple Lie algebra g, and let KC ! Aut(pC) be the complexi ed isotropy representation at the identity coset of the corresponding symmetric space. If e 2 pC is nilpotent, we consider the centralizer of e in KC. We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala-Carter classi cation of nilpo...

In view of the many applications of the theory of symmetric functions to representation theory it seems desirable to have a theory of symmetric functions in the spirit of Macdonald's book Mac] for Weyl groups other than the symmetric group. Our approach to this problem is to nd an algebraic structure which motivates each statement in the classical symmetric function theory. If this algebraic no...

Diagram algebras (e.g. graded braid groups, Hecke algebras, Brauer algebras) arise as tensor power centralizer algebras, algebras of commuting operators for a Lie algebra action on a tensor space. This work explores centralizers of the action of a complex reductive Lie algebra g on tensor space of the form M ⊗ N ⊗ V ⊗k. We define the degenerate two-boundary braid group Gk and show that centrali...

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

Given an n× n matrix A over a field F and a scalar a ∈ F , we consider the linear codes C(A, a) := {B ∈ F | AB = aBA} of length n2. We call C(A, a) a twisted centralizer code. We investigate properties of these codes including their dimensions, minimum distances, parity-check matrices, syndromes, and automorphism groups. The minimal distance of a centralizer code (when a = 1) is at most n, howe...

The centralizer C(w) of an elliptic element w in a Weyl group has a natural symplectic representation on the group of w-coinvariants in the root lattice. We give the basic properties of this representation, along with applications to p-adic groups—classifying maximal tori and computing inducing data in L-packets—as well as to elucidating the structure of the centralizer C(w) itself. We give the...

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 ...

We study the representation theory of the rook-Brauer algebra RBk(x), which has a of Brauer diagrams that allow for the possibility of missing edges. The Brauer, Temperley-Lieb, Motzkin, rook monoid, and symmetric group algebras are subalgebras of RBk(x). We prove that RBk(n+1) is the centralizer of the orthogonal group On(C) on tensor space and that RBk(n+1) and On(C) are in Schur-Weyl duality...

For a monoid M of k-valued unary operations, the centralizer M∗ is the clone consisting of all k-valued multi-variable operations which commute with every operation in M . First we give a sufficient condition for a monoid M to have the least clone as its centralizer. Then using this condition we determine centralizers of all monoids containing the symmetric group. AMS Mathematics Subject Classi...

In Section 2, after giving the basic definitions and some elementary consequences, we introduce two fundamental algebraic structures associated with a coherent configuration, namely, the boolean algebra of admissable relations and the adjacency ring. The action of a group on a finite set induces the structure of a coherent configuration in the set, and in this situations, which we refer to as t...