منابع مشابه
Graded 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 کاملUniversal Graded Specht Modules for Cyclotomic Hecke Algebras
The graded Specht module S for a cyclotomic Hecke algebra comes with a distinguished generating vector z ∈ S, which can be thought of as a “highest weight vector of weight λ”. This paper describes the defining relations for the Specht module S as a graded module generated by z. The first three relations say precisely what it means for z to be a highest weight vector of weight λ. The remaining r...
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 کاملPermutation resolutions for Specht modules
For every composition λ of a positive integer r , we construct a finite chain complex whose terms are direct sums of permutation modules M for the symmetric group Sr with Young subgroup stabilizers Sμ. The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ the chain complex has homology concentrated in one degree (at...
متن کاملSymmetric 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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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 2011
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crelle.2011.033