A note on symmetry classes of tensors and Specht modules

作者：Dias da Silva J A; Rodrigues Fatima; Silva Pedro C; Torres Maria M^*

来源：Linear Algebra and Its Applications, 2017, 531: 118-128.

DOI：10.1016/j.laa.2017.05.035

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

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.

• 出版日期2017-10-15