Nonstandard young tableaux of \(Γ_1 \)– non deranged permutation group \(G_p ^{Γ_1 }\)

  • Authors

    • Isah Abor Garba
    • Ojonugwa Ejima Usmanu Danfodiyo University, Sokoto, Nigeria
    • Kazeem Olalekan Aremu Usmanu Danfodiyo University, Sokoto
    • Usman Hamisu Usmanu Danfodiyo University, Sokoto
    2017-03-20
    https://doi.org/10.14419/gjma.v5i1.6632
  • Representations, Combinatorial Objects, Non - Standard Tableaux, Non-Deranged and Permutation Group.

  • Abstract

    There is a link between the representation of the permutation group  and the combinatorial object called Young tableaux. In this paper, we describe the representation of G1- non deranged permutation group via the Young tableaux, and we establish that every Young tableaux of this permutation group is not standard.

  • References

    1. [1] Aremu, K.O. Ahmad, R., Ejima, O. & Usman, H. (2016): Abstract group theoretical properties of - non deranged permutation group : Nigerian Journal of Basic and Applied Sciences.

      [2] Bruce, S (2001). The Symmetric Group: Rep resentations, Combinatorial Algorithms, and Symmetric Functions: Springer

      [3] Garba, A.I., & Ibrahim A.A (2010). A new method of constructing a Variety of Finite Group Based on Some Succession Scheme: International Journal of Physical Science 2(3) 23 – 26.

      [4] Heather, M.R., Matthew H. & Julianna, T. (2015). The Robinson Schensted Correspondence and A2-Web Bases. http://scholarship.richmond.edu/mathcs-faculty publications.

      [5] Ibrahim, A.A, Ejima, O, Aremu, K.O, (2016). On the Representations of – non deranged permutation group Advances in Pure Mathematics, 6, 608-614.

      [6] Ibrahim, A.A (2004). Group Theoretical In terpretation of Bara'at Model: Mathematical Association of Nigeria, Proceedings of Annual National Conference, 35 – 46.

      [7] Minkowski, H (1909). Space and time http://minkowskiinstitute.org/mip/books/

      [8] Okounkov, A., & Vershik, A. (1996). A new approach to representation theory of symmetric Groups: Selecta Math.,New Ser., 2, 581–605. https://doi.org/10.1007/bf02433451.

      [9] Quinton, W. (2008) Young’s Natural Representations of S4: arXiv: 1112.0687v1 [math.RT].

      [10] Usman, A. & Ibrahim, A.A (2011) a New Generating Function for Aunu Patterns: Application in Integer Group Modulo n. Nigerian Journal of Basic and Applied Sciences, 19(1): 1 – 4. https://doi.org/10.4314/njbas.v19i1.69337.

      [11] William, F. (1997). Young Tableaux with applications to representations theory and geometry: The Press Syndicate of the University of Cambridge.

      [12] Wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/Alfred-Young-disambiguation.

      [13] Wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/Frobenius’s-thoerem-(group-theory).

      [14] Xavier, B. & Nicolas, B. (2006) the unitary representations of the Poincar´e group in any spacetime dimension. arXiv:hep-th/0611263v1

      [15] Yufei, Z. (2008): Young Tableaux and the representations of the Symmetric Group. https://pdfs.semanticscholar.org/4703/420974ab8fcd6057f35644be9b251d35edd1.pdf.

  • Downloads

  • How to Cite

    Garba, I. A., Ejima, O., Olalekan Aremu, K., & Hamisu, U. (2017). Nonstandard young tableaux of \(Γ_1 \)– non deranged permutation group \(G_p ^{Γ_1 }\). Global Journal of Mathematical Analysis, 5(1), 21-23. https://doi.org/10.14419/gjma.v5i1.6632

    Received date: 2016-08-23

    Accepted date: 2016-09-22

    Published date: 2017-03-20