A note on symmetry classes of tensors and Specht modules

Fátima Rodrigues; J.A. Dias da Silva; Pedro C. Silva; Maria M. Torres

doi:10.1016/j.laa.2017.05.035

A note on symmetry classes of tensors and Specht modules

Fátima Rodrigues, J.A. Dias da Silva, Pedro C. Silva, Maria M. Torres

DM - Departamento de Matemática

Research output: Contribution to journal › Article › peer-review

Abstract

We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[S-m]-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.

Original language	English
Pages (from-to)	118-128
Number of pages	11
Journal	Linear Algebra and its Applications
Volume	531
DOIs	https://doi.org/10.1016/j.laa.2017.05.035
Publication status	Published - 15 Oct 2017

Keywords

Young tableau
Specht module
Symmetry class of tensors
Basic decomposable tensor
Orbital space

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10.1016/j.laa.2017.05.035Licence: CC BY-NC-ND

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title = "A note on symmetry classes of tensors and Specht modules",

abstract = "We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[S-m]-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. ",

keywords = "Young tableau, Specht module, Symmetry class of tensors, Basic decomposable tensor, Orbital space",

author = "F{\'a}tima Rodrigues and {Dias da Silva}, J.A. and Silva, {Pedro C.} and Torres, {Maria M.}",

note = "Sem PDF. Portuguese Funds through the FCT - Portuguese Foundation for Science and Technology (UID/MAT/00297/2013; PEst-OE/AGR/UI0239/2014; UID/MAT/04721/2013) ",

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journal = "Linear Algebra and its Applications",

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AU - Rodrigues, Fátima

AU - Dias da Silva, J.A.

AU - Silva, Pedro C.

AU - Torres, Maria M.

N1 - Sem PDF. Portuguese Funds through the FCT - Portuguese Foundation for Science and Technology (UID/MAT/00297/2013; PEst-OE/AGR/UI0239/2014; UID/MAT/04721/2013)

PY - 2017/10/15

Y1 - 2017/10/15

N2 - We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[S-m]-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.

AB - We construct induced bases for critical orbital spaces indexed by standard tableaux. As a corollary we obtain an explicit isomorphism of C[S-m]-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.

KW - Young tableau

KW - Specht module

KW - Symmetry class of tensors

KW - Basic decomposable tensor

KW - Orbital space

U2 - 10.1016/j.laa.2017.05.035

DO - 10.1016/j.laa.2017.05.035

M3 - Article

SN - 0024-3795

VL - 531

SP - 118

EP - 128

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

A note on symmetry classes of tensors and Specht modules

Abstract

Keywords

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