In this paper we study the branching problems for Hecke algebra H(Dn) of type Dn. We explicitly describe the decompositions of the socle of the restriction of each irreducible H(Dn)-representation to H(Dn−1) into irreducible modules by using the corresponding results for type B Hecke algebras. In particular, we show that any such restrictions are always multiplicity free.

Résumé. Le problème de la gestion des connaissances est un des problèmes les plus d’actualité dans les académiques et les industries. Plusieurs techniques constituent le socle opérationnel de ces problématiques. La technique d’ingénierie de connaissances MASK se présente comme la voie de recherche la plus prometteuse pour cerner ces problématiques de transfert, de partage et de capitalisation d...

This article is a contribution to the study of the automorphism groups of 2−(v, k, 1) designs. Let D be 2−(v, 13, 1) design, G ≤ Aut(D) be block transitive, point primitive but not flag transitive. Then Soc(G), the socle of G, is not classical simple group over finite filed GF (q)(q odd). Mathematics Subject Classification: 05B05, 20B25

We investigate the relationship between the facial structure of the unit ball of an operator algebra A and its algebraic structure, including the hereditary subalgebras and the socle of A. Many questions about the facial structure of A are studied with the aid of representation theory. For that purpose we establish the existence of reduced atomic type representations for certain nonselfadjoint ...

This note is part of a general programme to classify the automorphism groups of nite linear spaces. There have been a number of contributions to this programme including two recent surveys, 8, 3]. One of the most signiicant contributions was the classiication of ag-transitive linear spaces, 1]. Since then the eeort has been to classify the line-transitive examples. These fall naturally into two...

We show that in characteristic 2, the Steinberg representation of the symplectic group Sp 2n (q), q a power of an odd prime p, has two irreducible constituents lying just above the socle that are isomorphic to the two Weil modules of degree (qn −1)/2.

Let ∆ be a simplicial complex on V an n), where each ai ≥ 2. By utilizing the technique of Macaulay's inverse systems, we can explicitly describe the socle of A in terms of ∆. As a consequence, we determine the simplicial complexes, that we will call levelable, for which there exists a tuple (a1,. .. , an) such that A(∆, a1,. .. , an) is a level algebra.

Suppose that an automorphism group G acts flag-transitively on a finite generalized hexagon or octagon S, and suppose that the action on both the point and line set is primitive. We show that G is an almost simple group of Lie type, that is, the socle of G is a simple Chevalley group.

Let $G$ be an automorphism group of a‎ ‎$2$-$(v,k,4)$ symmetric design $mathcal D$‎. ‎In this paper‎, ‎we‎ ‎prove that if $G$ is flag-transitive point-primitive‎, ‎then the‎ ‎socle of $G$ cannot be an exceptional group of Lie type‎.