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Casimir operators for infinite-dimensional representations ofosp(1,2) andosp(1, 4) lie superalgebras

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Czechoslovak Journal of Physics B Aims and scope

Abstract

All independent Casimir operatorsK 2j , 1 ≦j ≦n, are considered for the Schurean ∞ -dimensional representations ofosp(1, 2n),n= 1,2, that were constructed recently. For these representations (which are expressed in terms of tensor products of linear differential operators andN byN matrices belonging to a finite set

and depending on a real parameterχ) a method is presented by which the “differential-operator part” of operators K2j is effectively eliminated and expressions for K2j via matrices in

are obtained. In the same way we treat the Casimir operators Ĉ2j of the even subalgebra sp(2n, ℝ) ⊂osp(1, 2n). The eigenvalues of K2j and Ĉ2j are evaluated as functions of the parameterχ for the representations of osp(1, 2) withN= 2 and ofosp(1, 4) withN = 2, 4.

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Authors and Affiliations

  1. Nuclear Centre, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 180 00, Praha 8, Czechoslovakia

    J. Blank

  2. Institute of Geology and Geotechnics, Czechosl. Acad. Sci., V Holešovičkách 41, 180 00, Praha 8, Czechoslovakia

    O. Navrátil

Authors
  1. J. Blank
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  2. O. Navrátil
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Blank, J., Navrátil, O. Casimir operators for infinite-dimensional representations ofosp(1,2) andosp(1, 4) lie superalgebras. Czech J Phys 36, 1003–1018 (1986). https://doi.org/10.1007/BF01597763

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  • DOI: https://doi.org/10.1007/BF01597763

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