publication . Article . Preprint . 2015

Signed Young modules and simple Specht modules

Kay Jin Lim; Susanne Danz;
Open Access
  • Published: 10 Apr 2015 Journal: Advances in Mathematics, volume 307, pages 369-416 (issn: 0001-8708, Copyright policy)
  • Publisher: Elsevier BV
Abstract
By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are parametrized by certain pairs of partitions. The main result of this article establishes the signed Young module labels of simple Specht modules. Along the way we prove a number of results concerning indecomposable signed Young modules that are of independent interest. In particular, we determine the label of the indecomposable signed Young module obtained by tensoring a given indecomposable signed Young module with the sign represent...
Subjects
arXiv: Mathematics::Representation TheoryAstrophysics::Galaxy Astrophysics
free text keywords: General Mathematics, Mathematics - Representation Theory, Vertex (geometry), Combinatorics, Symmetric group, Simple module, Indecomposable module, Specht module, Periodic graph (geometry), Mathematics
Funded by
EC| GLORY
Project
GLORY
Global-Local Methods in Representation Theory
  • Funder: European Commission (EC)
  • Project Code: 303774
  • Funding stream: FP7 | SP3 | PEOPLE
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