One of the main weakness of the family of centralizer codes is that its length is always n. Thus we have taken a new matrix equation code called intertwining code. Specialty of this code is the length of it, which is of the form nk. We establish two decoding methods which can be fitted to intertwining codes as well as for any linear codes. We also show an inclusion of linear codes into a specia...

The main result in this note is that if X is a simple loop in the boundary of a compact, irreducible, orientable 3-manifold M and [X] ¥= 1 G trx(M), one can represent the centralizer of [X] in irx(M) by a Seifert fibred submanifold of M. Introduction. The main result in this note is a partial answer to a question of Jaco [2]. Jaco has shown in [2] that the centralizer of a nontrivial element in...

In this paper, given a split extension of an arbitrary Coxeter group by automorphisms of the Coxeter graph, we determine the involutions in that extension whose centralizer has finite index. Our result has applications to many problems such as the isomorphism problem of general Coxeter groups. In the argument, some properties of certain special elements and of the fixed-point subgroups by graph...

We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’...

In this paper, we show that for every abelian subgroup H of a Garside group, some conjugate gHg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems conc...

Let be a finitely generated abelian-by-finite group and k a field of characteristic p 0. We show that the Euler class of over k has finite order if and only if every p-regular element of has infinite centralizer in . We also give a lower bound for the order of the Euler class in terms of suitable finite subgroups of . This lower bound is derived from a more general result on finite-dimensional ...

According to a conjecture of Lusztig, the asymptotic affine Hecke algebra should admit description in terms Grothedieck group sheaves on square finite set equivariant under action centralizer nilpotent element reductive group. A weaker form this statement, allowing for possible central extensions stabilizers that action, has been proved by first named author with Ostrik. In present paper we des...