where the LGLn(λ) are irreducible GLn(C)-modules and the S λ k are irreducible Sk-modules. The decomposition in (0.1) essentially makes the study of the representations of GLn(C) and the study of representations of the symmetric group Sk two sides of the same coin. The group GLn(C) has interesting subgroups, GLn(C) ⊇ On(C) ⊇ Sn ⊇ Sn−1, and corresponding centralizer algebras, CSk ⊆ CBk(n) ⊆ CAk(...

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...

INTRODUCTION Femoral centralizers in total hip arthroplasty (THA) are designed to improve the neutral implant position and ensure a homogeneous cement mantle without implant-bone impingement. To date there are no data about the cement mantle configuration and implant position after malinsertion, as seen in mini-open approaches or adipose patients with a limited view. The present biomechanical s...

Introduction 1 1. Representation Theory of Finite Groups 2 1.1. Preliminaries 2 1.2. Group Algebra 4 1.3. Character Theory 5 2. Irreducible Representations of the Symmetric Group 8 2.1. Specht Modules 8 2.2. Dimension Formulas 11 2.3. The RSK-Correspondence 12 3. Schur-Weyl Duality 13 3.1. Representations of Lie Groups and Lie Algebras 13 3.2. Schur-Weyl Duality for GL(V ) 15 3.3. Schur Functor...

We describe the isomorphism class of the torus centralizing a regular, semi-simple, stable conjugacy class in a simply-connected, semi-simple group. Let k be a field, and let G be a semi-simple, simply-connected algebraic group, which is quasi-split over k. The theory of semi-simple conjugacy classes in G is well understood, from work of Steinberg [S] and Kottwitz [K]. Any semi-simple conjugacy...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of the group of unitary operations to present a private-key quantum homomorphic encryption scheme that hides arbitrary quantum computations. A particular instance of our encoding hides information at least proportional to m/ log...

We study centralizers of elements in domains. We generalize a result of the author and Small [4], showing that if A is a finitely generated noetherian domain and a ∈ A is not algebraic over the extended centre of A then the centralizer of a has Gelfand-Kirillov dimension at most one less than the Gelfand-Kirillov dimension of A. In the case that A is a finitely generated noetherian domain of GK...

We survey the known results on two old open problems on commutation of languages. The first problem, raised by Conway in 1971, is asking if the centralizer of a rational language must be rational as well – the centralizer of a language is the largest set of words commuting with that language. The second problem, proposed by Ratoandromanana in 1989, is asking for a characterization of those lang...

Let X and Y be commuting nilpotent K-endomorphisms of a vector space V , where K is a field of characteristic p ≥ 0. If F = K(t) is the field of rational functions on the projective line P1/K , consider the K(t)-endomorphism A = X+ tY of V . If p = 0, or if A = 0, we show here that X and Y are tangent to the unipotent radical of the centralizer of A in GL(V ). For all geometric points (a : b) o...