The real compact supergroup S^1|1 is analysed from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of (C1|1)× with reduced Lie group S^1, and a link with SUSY structures on C^1|1 is established. We describe a large family of complex semisimple representations of S^1|1 and we show that any S^1|1-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for S^1|1
SUSY structures, representations and Peter-Weyl theorem for S1|1
CARMELI, CLAUDIO;
2015-01-01
Abstract
The real compact supergroup S^1|1 is analysed from different perspectives and its representation theory is studied. We prove it is the only (up to isomorphism) supergroup, which is a real form of (C1|1)× with reduced Lie group S^1, and a link with SUSY structures on C^1|1 is established. We describe a large family of complex semisimple representations of S^1|1 and we show that any S^1|1-representation whose weights are all nonzero is a direct sum of members of our family. We also compute the matrix elements of the members of this family and we give a proof of the Peter-Weyl theorem for S^1|1
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