Multiplicity-free representations and coisotropic actions of certain nilpotent Lie groups over quasi-symmetric Siegel domains

Abstract

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.

31 pages. /v2: improved presentation and updated references/ v3: improved introduction and updated references, fully revised version will appear in Complex Analysis and Operator Theory

References in corpus (5)

• Visible actions on symmetric spaces
• Propagation of multiplicity-freeness property for holomorphic vector bundles
• A generalized Cartan decomposition for the double coset space U(n_1) x U(n_2) x U(n_3)) U(n) / U(p) x U(q)
• Classification of multiplicity free symplectic representations
• Polar symplectic representations