Czechoslovak Journal of Physics B

, Volume 39, Issue 11, pp 1192–1207 | Cite as

On the tensor product of supersingleton representations ofosp(1, 2n)

  • J. Blank
  • M. Havlíček


The tensor product of two supersingleton representationsσn of the Lie superalgebraosp (1, 2n) is studied forn≧2. The main results are as follows: (a) anticommutators and commutators of the odd generators inσn⊗ σn form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components ofσnσn, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals\(\left( \begin{gathered} J + n - 1 \hfill \\ n - 1 \hfill \\ \end{gathered} \right)\), i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).


Tensor Product Basic Property Explicit Form Irreducible Component Massless Representation 
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Copyright information

© Academia, Publishing House of the Czechoslovak Academy of Sciences 1989

Authors and Affiliations

  • J. Blank
    • 1
  • M. Havlíček
    • 2
  1. 1.Nuclear CentreCharles UniversityPraha 8Czechoslovakia
  2. 2.Department of Mathematics, Faculty of Nuclear Science and Physical EngineeringCzech Technical UniversityPraha 2Czechoslovakia

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