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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Reflection positivity for unitary representations of Lie groups
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by Humberto Prado PDF
Proc. Amer. Math. Soc. 114 (1992), 723-731 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • 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