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<p>We study multiplicity-free representations of Lie groups over a quasi-symmetric Siegel domain, with a focus on certain two-step nilpotent Lie groups. We provide necessary and sufficient conditions for the multiplicity-freeness property to hold. Specifically, we establish the equivalence between the disjointness of irreducible unitary representations realized over the domain, the multiplicity-freeness of the unitary representation on the Bergman space, and the coisotropicity of the group action.</p>

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Multiplicity-Free Representations and Coisotropic Actions of Certain Nilpotent Lie Groups over Quasi-Symmetric Siegel Domains

  • 期刊论文

  • 发表日期：

    2025年3月21日

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  • Koichi Arashi

摘要

We study multiplicity-free representations of Lie groups over a quasi-symmetric Siegel domain, with a focus on certain two-step nilpotent Lie groups. We provide necessary and sufficient conditions for the multiplicity-freeness property to hold. Specifically, we establish the equivalence between the disjointness of irreducible unitary representations realized over the domain, the multiplicity-freeness of the unitary representation on the Bergman space, and the coisotropicity of the group action.