Reflection Positive Distribution Vectors

  • Karl-Hermann NeebEmail author
  • Gestur Ólafsson
Part of the SpringerBriefs in Mathematical Physics book series (BRIEFSMAPHY, volume 32)


In this chapter we first introduce the concept of a distribution vector of a unitary representation (Sect. 7.1). It turns out that certain distribution vectors semi-invariant under a subgroup H correspond naturally to realizations of the representation in a Hilbert space of distributions on the homogeneous space G / H. In this context reflection positive representations can be constructed from reflection positive distributions on G / H (Sect. 7.2). Such distributions can often be found and even classified in terms of the geometry of the homogeneous space.

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Department MathematikUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA

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