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

Gang Liu; Spyridon Afentoulidis-Almpanis

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

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arxiv 2502.19968 v1 pith:CNDZ6GZS submitted 2025-02-27 math.RT

Spyridon Afentoulidis-Almpanis , Gang Liu This is my paper · ORCID

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abstract

We provide an explicit direct integral decomposition for the tensor product representation $\pi_1\widehat{\otimes}\pi_2$ of the rank one spin group $\mathrm{Spin}(n,1)$ whenever $\pi_1$ is a unitary principal series representation and $\pi_2$ is an arbitrary irreducible unitary representation of $\mathrm{Spin}(n,1)$.

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