On the tensor product of supersingleton representations ofosp(1, 2n) |
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Authors: | J Blank M Havlí?ek |
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Institution: | (1) Nuclear Centre, Charles University, V Holeovikách 2, 180 00 Praha 8, Czechoslovakia;(2) Department of Mathematics, Faculty of Nuclear Science and Physical Engineering, Czech Technical University, Trojanova 13, 120 00 Praha 2, Czechoslovakia |
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Abstract: | The tensor product of two supersingleton representations
n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in
n
n form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of
n
n, 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
, 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).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday. |
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