We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl n and sln, and give a complete reducibility result. These quantum groups have a natural n-dimensional module V . We prove an analogue of Schur-Weyl duality in this setting: the centralizer algebra of the quantum group action on the k-fold ten...

We prove that the centralizer of a Coxeter element in an irreducible group is cyclic generated by element.

We analyze the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik’s commuting algebra of difference operators via an analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are defined and realized as solutions to the system of basic hypergeometric difference equatio...

BACKGROUND AND PURPOSE A proximal stem centralizer may be beneficial regarding cementing pressures, cement penetration, and stem alignment. We measured these parameters when cementing a mat-surfaced femoral component with and without the use of a proximal stem centralizer. MATERIAL AND METHODS 8 femoral prostheses with proximal centralizers and 8 femoral prostheses without proximal centralize...

We prove a global fixed point theorem for the centralizer of a homeomorphism of the two dimensional disk D that has attractor-repeller dynamics on the boundary with at least two attractors and two repellers. As one application, we show that there is a finite index subgroup of the centralizer of a pseudo-Anosov homeomorphism with infinitely many global fixed points. As another application we giv...

Abstract. We consider semidefinite programming problems on which a permutation group is acting. We describe a general technique to reduce the size of such problems, exploiting the symmetry. The technique is based on a low-order matrix ∗-representation of the commutant (centralizer ring) of the matrix algebra generated by the permutation matrices. We apply it to extending a method of de Klerk et...

A group G is called power commutative, or a PC-group, if [xm, yn] = 1 implies [x, y] = 1 for all x, y ∈G such that xm = 1, yn = 1. So power-commutative groups are those groups in which commutativity of nontrivial powers of two elements implies commutativity of the two elements. Clearly, G is a PC-group if and only if CG(x) = CG(x) for all x ∈ G and all integers n such that xn = 1. Obvious examp...

Olshanski' s centralizer construction provides a realization of the Yangian Y(m) for the Lie algebra gl(m) as a subalgebra in the projective limit algebra A m = lim proj A m (n) as n → ∞, where A m (n) is the centralizer of gl(n − m) in the enveloping algebra U(gl(n)). We give a modified version of this construction based on a quantum analog of Sylvester's theorem. We then use it to get an alge...