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Reflection positivity for unitary representations of Lie groups


Author: Humberto Prado
Journal: Proc. Amer. Math. Soc. 114 (1992), 723-731
MSC: Primary 22E45; Secondary 46N99, 47A67, 53C35
DOI: https://doi.org/10.1090/S0002-9939-1992-1072089-6
MathSciNet review: 1072089
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Abstract: Let $ G$ be a Lie group, and let $ \sigma $ be an involutive automorphism on $ G$. Then we establish a correspondence between unitary representations of $ G$ and unitary representations of a simply connected Lie group $ {G^*}$ dual to $ G$, where the duality is defined by the given involution $ \sigma $. The correspondence is obtained from a geometric assumption that was considered earlier in connection with reflection positivity. As a consequence of this construction, we obtain unitary representations of universal covering groups.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1072089-6
Keywords: Local representations, symmetric spaces, reflection positivity, induced representations and phrases
Article copyright: © Copyright 1992 American Mathematical Society

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