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On a construction of young modules
thesisposted on 2014-12-15, 10:40 authored by Marie Vernon
Let n be a natural number and E an n-dimensional vector space over a field K. The symmetric group acts by place permutation on the tensor space E âŠ—r. The Sigmar-module EâŠ—r can be decomposed into a direct sum of permutation modules Mlambda where lambda is a composition of r into at most n parts.;Each permutation module labelled by such a composition is isomorphic to one labelled be a partition of r into at most n parts, and therefore we assume that lambda is such a partition. The indecomposable direct summands of the permutation module M lambda are called Young modules, and they are labelled by partitions of r into at most n parts.;Throughout this thesis we consider the case where E has dimension two. For lambda a two-part partition of r, we explicitly decompose the module M lambda into a direct sum of Young modules by providing spanning sets for the Young modules.;Moreover, we consider the problem of finding a basis or an algorithm for a basis for the Young modules in this case and, although we have not been able to solve this in general, we give some conjectures and examples showing in which cases we can find a basis.
Date of award2005-01-01
Awarding institutionUniversity of Leicester