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The Eigenspaces of the Bose-Mesner-Algebras of the Association Schemes Corresponding to Projective Spaces and Polar Spaces

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Abstract

In an earlier paper 7, some properties of the eigenspaces of the Bose-Mesner-algebras of association schemes are figured out, leaving open the problem of determining the eigenspaces. In the present paper, these eigenspaces and the eigenvalues are determined for projective spaces and for polar spaces. This allows characterizations of certain sets of subspaces of these geometries.

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References

  1. R. C. Bose and D. M. Mesner, On linear associative algebras corresponding to association schemes of partially balanced designs, Ann. Math. Statist., Vol. 30 (1959) pp. 21-38.

    Google Scholar 

  2. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-regular graphs, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 18, Springer Verlag, Berlin (1989).

    Google Scholar 

  3. P. J. Cameron, Projective and polar spaces, QMW Math Notes, Vol. 13, School of Mathematical Sciences, Queen Mary and Westfield College London.

  4. P. J. Cameron, R. A. Liebler, Tactical decompositions and orbits of projective groups, Lin. Alg. Appl., Vol. 46 (1982) pp. 91-102.

    Google Scholar 

  5. P. Delsarte, Association schemes and t-designs in regular semilattices, J. Comb. Theory (A), Vol. 20 (1976) pp. 230-243.

    Google Scholar 

  6. J. Eisfeld, On the common nature of spreads and pencils in PG(d, q), Discrete Mathematics, Vol. 189 (1998) pp. 95-104.

    Google Scholar 

  7. J. Eisfeld, Subsets of association schemes corresponding to eigenvectors of the Bose-Mesner algebra, Bull. Belg. Math. Soc., Vol. 5 (1998) pp. 265-274.

    Google Scholar 

  8. J. Eisfeld, Theorie der Cliquoide in stark regulären Graphen, Assoziationsschemata, partiellen geometrischen Designs, projektiven Räumen und Polarräumen, Inaugural-Dissertation, Justus-Liebig-Universität Gießen 1997.

  9. W. M. Kantor, On incidence matrices of finite projective and affine spaces, Math. Z., Vol. 124 (1972) pp. 315-318.

    Google Scholar 

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  1. Mathematisches Institut, Arndtstr. 2, D-35392, Gie, Germany

    Jörg Eisfeld

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  1. Jörg Eisfeld
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Eisfeld, J. The Eigenspaces of the Bose-Mesner-Algebras of the Association Schemes Corresponding to Projective Spaces and Polar Spaces. Designs, Codes and Cryptography 17, 129–150 (1999). https://doi.org/10.1023/A:1008366907558

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  • DOI: https://doi.org/10.1023/A:1008366907558

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