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Computation of the Dimensions of Symmetry Classes of Tensors Associated with the Finite two Dimensional Projective Special Linear Group

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

The dimensions of the symmetry classes of tensors associated with the projective special linear group of degree 2 over a field with q elements, PSL 2(q), are found. Of course we will assume PSL 2(q) as a subgroup of the symmetric group S q +1 because this group has a faithful action on the points of the underlying projective space. We also discuss the non-triviality of the symmetry classes of tensors associated with each irreducible character of PSL 2(q).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Tehran & Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran (e-mail: darafshe, pournaki@vax.ipm.ac.ir), , , , , , IR

    M. R. Darafsheh & M. R. Pournaki

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  1. M. R. Darafsheh
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  2. M. R. Pournaki
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Received: October 14, 1998; revised version: November 30, 1999

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Darafsheh, M., Pournaki, M. Computation of the Dimensions of Symmetry Classes of Tensors Associated with the Finite two Dimensional Projective Special Linear Group. AAECC 10, 237–250 (2000). https://doi.org/10.1007/s002000050127

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  • DOI: https://doi.org/10.1007/s002000050127

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