Invariant Hilbert spaces of distribution vectors in Lie group representations

2025/07/08 by Ingrid Beltiţă, Beltita, Ingrid, Daniel Beltiţă +1
Mathematics · #22E25 #46F10 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Primary 22E27 #Representation Theory (math.RT) #Secondary 17B30

paper · pdf · doi:10.48550/arxiv.2507.05988

openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every unitary irreducible representation of a Lie group we prove that the representation Hilbert space is the only nonzero invariant Hilbert space of distribution vectors.

Citations

• Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

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