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 (C^1|1)×(C^1|1)× with reduced Lie group S1, 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
R. Fioresi, C. Carmeli, S. D. Kwok (2015). SUSY structures, representations and Peter-Weyl theorem for S^1|1. JOURNAL OF GEOMETRY AND PHYSICS, 95, 144-158.
SUSY structures, representations and Peter-Weyl theorem for S^1|1
FIORESI, RITA;
2015
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 (C^1|1)×(C^1|1)× with reduced Lie group S1, 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|1I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
