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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
Article
  • 11 Downloads

Abstract

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).

Keywords

Tensor Product Basic Property Explicit Form Irreducible Component Massless Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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