poster: SUSY structures, representations and the Peter-Weyl theorem for \(S^{(1|1)}\)

speaker: Stephen Kwok (Univ. of Luxembourg)

abstract: We study the real supergroup \(S^{(1
1)}\) and its representation theory from various perspectives. We prove that it is the unique (up to isomorphism) real form of \((\mathbb{C}^{(1
1)})^\times\) with reduced group \(S^1\), and relate it to SUSY-structures. We also show complete reducibility for \(S^{(1
1)}\) representations whose weights are all nonzero, and use this to prove the Peter-Weyl theorem for \(S^{(1
1)}\). This is joint work with C. Carmeli (Genoa) and R. Fioresi (Bologna).

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