The centralizer of a set of words X is the largest set of words C(X) commuting with X: XC(X) = C(X)X. It has been a long standing open question due to Conway, 1971, whether the centralizer of any rational set is rational. While the answer turned out to be negative in general, see Kunc 2004, we prove here that the situation is different for codes: the centralizer of any rational code is rational...

In our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We study the ‘stable’ properties of the centralizers of S(n − m) in the group algebra C[S(n)] as n → ∞ with m fixed. We construct a limit centralizer algebra A...

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...

In this article, we provide counterexamples to a conjecture of M. Pellegrini and P. Shumyatsky which states that each coset the centralizer an involution in finite non-abelian simple group $G$ contains odd order element, unless $G=\text{PSL}(n,2)$ for $n\geq 4$. More precisely, show does not hold alternating $A_{8n}$ all 2$.

In [I] we introduced the notion of transfer from a group over a local field to an associated endoscopic group, but did not prove its existence, nor do we do so in the present paper. Nonetheless we carry out what is probably an unavoidable step in any proof of existence: reduction to a local statement at the identity in the centralizer of a semisimple element, a favorite procedure of Harish Chan...

A p–compact group (see Dwyer–Wilkerson [8]) is a loop space X such that X is Fp –finite and that its classifying space BX is Fp –complete (see Andersen–Grodal– Møller–Viruel [2] and Dwyer–Wilkerson [11]). We recall that the p–completion of a compact Lie group G is a p–compact group if π0(G) is a p–group. Next, if C(ρ) denotes the centralizer of a group homomorphism ρ from a p–toral group to a c...