Merigon S, Neeb KH, Salmasian H (2012)
Publication Type: Journal article, Original article
Publication year: 2012
Book Volume: 257
Pages Range: 431 - 469
Journal Issue: 2
We prove that the categories of smooth and analytic unitary representations of Banach--Lie supergroups are well-behaved under restriction functors, in the sense that the restriction of a representation to an integral subsupergroup is well-defined. We also prove that the category of analytic representations is isomorphic to a subcategory of the category of smooth representations. These facts are needed as a crucial first step to a rigorous treatment of the analytic theory of unitary representations of Banach--Lie supergroups. They extend the known results for finite dimensional Lie supergroups. In the infinite dimensional case the proofs require several new ideas. As an application, we give an analytic realization of the oscillator representation of the restricted orthosymplectic Banach--Lie supergroup.
APA:
Merigon, S., Neeb, K.H., & Salmasian, H. (2012). Categories of unitary representations of Banach-Lie supergroups and restriction functors. Pacific Journal of Mathematics, 257(2), 431 - 469. https://dx.doi.org/10.2140/pjm.2012.257.431
MLA:
Merigon, Stephane, Karl Hermann Neeb, and Hadi Salmasian. "Categories of unitary representations of Banach-Lie supergroups and restriction functors." Pacific Journal of Mathematics 257.2 (2012): 431 - 469.
BibTeX: Download