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Unitary lowest weight representations of the noncompact supergroup \(OSp(2m^*/2n)\). (English) Zbl 0741.22016

Unitary lowest weight representations of noncompact Lie superalgebras and supergroups seem to play an important role in supersymmetry theories. The oscillator construction for such irreducible representations is given, for the Lie supergroup \(Osp(2m^*/2n)\), with even subgroup \(SO^*(2m)\times USp(2n)\). Decomposition rules to the even subgroup are given, and considered in more detail for the examples \(Osp(4^*/2)\) and \(Osp(4^*/6)\).

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
17A70 Superalgebras
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[1] DOI: 10.1016/0370-2693(82)91170-4 · doi:10.1016/0370-2693(82)91170-4
[2] DOI: 10.1016/0370-2693(82)91170-4 · doi:10.1016/0370-2693(82)91170-4
[3] DOI: 10.1007/BF01206048 · Zbl 0531.17002 · doi:10.1007/BF01206048
[4] DOI: 10.1016/0550-3213(85)90129-4 · doi:10.1016/0550-3213(85)90129-4
[5] DOI: 10.1016/0550-3213(86)90342-1 · doi:10.1016/0550-3213(86)90342-1
[6] DOI: 10.1088/0264-9381/2/2/001 · doi:10.1088/0264-9381/2/2/001
[7] DOI: 10.1016/0550-3213(86)90293-2 · doi:10.1016/0550-3213(86)90293-2
[8] DOI: 10.1088/0264-9381/2/1/003 · doi:10.1088/0264-9381/2/1/003
[9] DOI: 10.1088/0264-9381/2/1/003 · doi:10.1088/0264-9381/2/1/003
[10] DOI: 10.1016/0370-2693(78)90894-8 · Zbl 1156.83327 · doi:10.1016/0370-2693(78)90894-8
[11] DOI: 10.1063/1.528120 · Zbl 0681.22018 · doi:10.1063/1.528120
[12] DOI: 10.1063/1.527920 · Zbl 0655.17009 · doi:10.1063/1.527920
[13] DOI: 10.1016/0001-8708(77)90017-2 · Zbl 0366.17012 · doi:10.1016/0001-8708(77)90017-2
[14] DOI: 10.1016/0550-3213(89)90421-5 · doi:10.1016/0550-3213(89)90421-5
[15] DOI: 10.1063/1.525508 · Zbl 0488.22040 · doi:10.1063/1.525508
[16] DOI: 10.1063/1.525508 · Zbl 0488.22040 · doi:10.1063/1.525508
[17] DOI: 10.1063/1.525508 · Zbl 0488.22040 · doi:10.1063/1.525508
[18] DOI: 10.1063/1.525508 · Zbl 0488.22040 · doi:10.1063/1.525508
[19] DOI: 10.1063/1.525508 · Zbl 0488.22040 · doi:10.1063/1.525508
[20] DOI: 10.1016/0550-3213(84)90164-0 · Zbl 1223.81116 · doi:10.1016/0550-3213(84)90164-0
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