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Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 921-933, 2020

Generalized symmetry classes of tensors

Gholamreza Rafatneshan, Yousef Zamani

Received January 29, 2019.   Published online July 8, 2020.
Abstract:  Let $V$ be a unitary space. For an arbitrary subgroup $G$ of the full symmetric group $S_m$ and an arbitrary irreducible unitary representation $\Lambda$ of $G$, we study the generalized symmetry class of tensors over $V$ associated with $G$ and $\Lambda$. Some important properties of this vector space are investigated.
Keywords:  irreducible character; generalized Schur function; orthogonal basis; symmetry class of tensors
Classification MSC:  20C30, 15A69
DOI:  10.21136/CMJ.2020.0044-19
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Affiliations:   Gholamreza Rafatneshan, Yousef Zamani (corresponding author), Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, P.O.Box 51335/1996, Sahand New Town, Tabriz, East Azerbaijan, Iran, e-mail: gh_rafatneshan@sut.ac.ir, zamani@sut.ac.ir
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