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@article{faucris.258801811,
abstract = {A visible action on a complex manifold is a holomorphic action that admits a J -transversal totally real submanifold S . It is said to be strongly visible if there exists an orbitpreserving anti-holomorphic diffeomorphism σ such that σjS = idS . Let G be the Heisenberg group and H a non-trivial connected closed subgroup of G. We prove that any complex homogeneous space D = GC/HC admits a strongly visible L-action, where L stands for a connected closed subgroup of G explicitly constructed through a co-exponential basis of H in G. This leads in turn that G itself acts strongly visibly on D. The proof is carried out by finding explicitly an orbit-preserving anti-holomorphic diffeomorphism and a totally real submanifold S , for which the dimension depends upon the dimensions of G and H. As a direct application, our geometric results provide a proof of various multiplicity-free theorems on continuous representations on the space of holomorphic sections on D. Moreover, we also generate as a consequence, a geometric criterion for a quasi-regular representation of G to be multiplicity-free.},
author = {Baklouti, Ali and Sasaki, Atsumu},
faupublication = {yes},
journal = {Journal of Lie Theory},
keywords = {Heisenberg group; Heisenberg homogeneous space; Multiplicityfree representation; Slice; Visible action},
note = {CRIS-Team Scopus Importer:2021-05-21},
pages = {719-750},
peerreviewed = {Yes},
title = {{Visible} actions and criteria for multiplicity-freeness of representations of heisenberg groups},
volume = {31},
year = {2021}
}