Vertices of Specht modules
نویسندگان
چکیده
منابع مشابه
Vertices of Specht Modules and Blocks of the Symmetric Group
This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A corollary of this theorem is a new way to determine the defect groups of symmetric groups. The main theorem is also used to find the Green correspondents of...
متن کاملTwo theorems on the vertices of Specht modules
Two theorems about the vertices of indecomposable Specht modules for the symmetric group, defined over a field of prime characteristic p, are proved: 1. The indecomposable Specht module S has non-trivial cyclic vertex if and only if λ has p-weight 1. 2. If p does not divide n and S(n−r,1 ) is indecomposable then its vertex is a p-Sylow subgroup of Sn−r−1 × Sr. Mathematics Subject Classification...
متن کاملSpecht modules and chromatic polynomials
An explicit formula for the chromatic polynomials of certain families of graphs, called ‘bracelets’, is obtained. The terms correspond to irreducible representations of symmetric groups. The theory is developed using the standard bases for the Specht modules of representation theory, and leads to an effective means of calculation. MSC 2000: 05C15, 05C50.
متن کاملGraded Specht Modules
Recently, the first two authors have defined a Z-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l, 1, d). In this paper we explain how to grade Specht modules over these algebras.
متن کاملElementary divisors of Specht modules
The irreducible representations of the symmetric groups and their Iwahori-Hecke algebras have been classified and constructed by James [6] and Dipper and James [2], yet simple properties of these modules, such as their dimensions, are still not known. Every irreducible representation of these algebras is constructed by quotienting out the radical of a bilinear form on a particular type of modul...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1984
ISSN: 0021-8693
DOI: 10.1016/0021-8693(84)90057-7