Globalisations of Supermodules

What is it about?

For any Lie supergroup whose underlying Lie group is reductive, we prove an extension of the Casselman–Wallach globalisation theorem: there is an equivalence between the category of Harish-Chandra modules and the category of SFSF-representations (smooth Fréchet representations of moderate growth) whose module of finite vectors is Harish-Chandra. As an application, we extend to Lie supergroups a general form of the Gel′fand–Kazhdan criterion due to Sun–Zhu.

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