Tensor product decomposition for rank-one spin groups I : unitary principal series representations

2025/02/27 by Spyridon Afentoulidis-Almpanis, Gang Liu, Afentoulidis-Almpanis, Spyridon +1
Mathematics · #22E30 #22E46 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2502.19968

openalex publication_date 2025/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an explicit direct integral decomposition for the tensor product representation π₁\widehat⊗π₂ of the rank one spin group Spin(n,1) whenever π₁ is a unitary principal series representation and π₂ is an arbitrary irreducible unitary representation of Spin(n,1).

Related

• Tensor products of complementary series of rank one Lie groups
• Saturation and Irredundancy for Spin(8)
• Restriction of irreducible unitary representations of Spin(N,1) to parabolic subgroups
• On the saturation conjecture for Spin(2n)
• Holomorphic Discrete Series of SU(1,1): Orthogonality Relations, Character Formulas, and Multiplicities in Tensor Product Decompositions