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On fine gradings and their symmetries

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Czechoslovak Journal of Physics Aims and scope

Abstract

In this paper fine gradings ofgl(n, C) associated with the Pauli matrices inn dimensions are studied with the subsequent graded contractions ofsl(n, C) in view. It is shown that, ifn≥3 is a prime, the discrete symmetries of the gradings involve the specialn-dimensional representations ofSL(2,F n), whereF n is the finite field of ordern. These symmetries may be used to simplify the system of contraction equations.

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Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128 – A, H3C 3J7, Montréal, Québec, Canada

    J. Patera

  2. Doppler Institute for Mathematical Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, Břehová 7, CZ-115 19, Praha, Czech Republic

    M. Havlíček, E. Pelantová & J. Tolar

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  1. J. Patera
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  2. M. Havlíček
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  3. E. Pelantová
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  4. J. Tolar
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Patera, J., Havlíček, M., Pelantová, E. et al. On fine gradings and their symmetries. Czech J Phys 51, 383–391 (2001). https://doi.org/10.1023/A:1017501925328

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  • DOI: https://doi.org/10.1023/A:1017501925328

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