SUSY structures, representations and Peter-Weyl theorem for S1|1

JOURNAL OF GEOMETRY AND PHYSICS

卷:95

Article

Carmeli, C.¹  Fioresi, R.²  Kwok, S.³ 

[1] Univ Genoa, DIME, I-17100 Savona, Italy

[2] Univ Bologna, Dipartimento Matemat, I-40126 Bologna, Italy

[3] Univ Luxembourg, Math Res Unit, L-1359 Luxembourg, Luxembourg

关键词: Lie supergroups;    SUSY structures;    Representations of Lie supergroups;   

DOI  :  10.1016/j.geomphys.2015.05.005

来源: Elsevier

【 摘 要 】

The real compact supergroup S-1 vertical bar 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 vertical bar 1)(x) with reduced Lie group S-1, and a link with SUSY structures on C-1 vertical bar 1 is established. We describe a large family of complex semisimple representations of S-1 vertical bar 1 and we show that any S-1 vertical bar 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 vertical bar 1. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free