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.

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 ...

A complete extension theorem for linear codes over a module alphabet and the symmetrized weight composition is proved. It is shown that an extension property with respect to arbitrary weight function does not hold for module alphabets with a noncyclic socle.

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 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.