Symmetric Group Modules with Specht and Dual Specht Filtrations
نویسندگان
چکیده
منابع مشابه
Symmetric Group Modules with Specht and Dual Specht Filtrations
The author and Nakano recently proved that multiplicities in a Specht filtration of a symmetric group module are well-defined precisely when the characteristic is at least five. This result suggested the possibility of a symmetric group theory analogous to that of good filtrations and tilting modules for GLn(k). This paper is an initial attempt at such a theory. We obtain two sufficient conditi...
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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 کاملThe Complexity of Certain Specht Modules for the Symmetric Group
During the 2004-2005 academic year the VIGRE algebra research group at the University of Georgia computed the complexities of certain Specht modules S for the symmetric group Σd, using the computer algebra program Magma. The complexity of an indecomposable module does not exceed the p-rank of the defect group of its block. The Georgia group conjectured that, generically, the complexity of a Spe...
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.
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2007
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870701410611