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Twisted Reflection Positivity, Mostafa Ahmad Hayajneh

LSU Doctoral Dissertations

Reflection positivity has several applications in both mathematics and physics. For example, reflection positivity induces a duality between group representations. In this thesis, we coin a new definition for a new kind of reflection positivity, namely, twisted reflection positive representation on a vector space. We show that all of the non-compactly causal symmetric spaces give rise to twisted reflection positive representations. We discover examples of twisted reflection positive representations on the sphere and on the Grassmannian manifold which are not unitary, namely, the generalized principle series with the Cosine transform as an intertwining operator. We give a direct proof for …