A note on symmetry classes of tensors and Specht modules

We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[Sm]-modules between Specht modules and critical orbital spaces which yields a realization of the complete set of complex irreducible representations of the symme...

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Bibliographic Details
Published in:Linear algebra and its applications 2017-10, Vol.531, p.118-128
Main Authors: Dias da Silva, J.A., Rodrigues, Fátima, Silva, Pedro C., Torres, Maria M.
Format: Article
Language:English
Subjects:
Basic decomposable tensor
Construction standards
Geometry
Isomorphism
Linear algebra
Mathematical analysis
Modules
Orbital space
Specht module
Symmetry
Symmetry class of tensors
Tensors
Vector space
Young tableau
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Summary:We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[Sm]-modules between Specht modules and critical orbital spaces which yields a realization of the complete set of complex irreducible representations of the symmetric group in terms of decomposable symmetrized tensors.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.05.035