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We investigate the multiplicity-freeness property for the holomorphic multiplier representations of affine transformation groups of a Siegel domain of the second kind. We deal with the generalized Heisenberg group and its subgroups. This property is explored in relation to the geometrical notions of coisotropic action and visible action, and also the commutativity of the algebra of invariant differential operators.

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Multiplicity-Free Representations of Certain Nilpotent Lie Groups Over Siegel Domains of the Second Kind

  • 会议论文

  • 发表日期：

    2026年

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  • Koichi Arashi

摘要

We investigate the multiplicity-freeness property for the holomorphic multiplier representations of affine transformation groups of a Siegel domain of the second kind. We deal with the generalized Heisenberg group and its subgroups. This property is explored in relation to the geometrical notions of coisotropic action and visible action, and also the commutativity of the algebra of invariant differential operators.