caa a22 4500 605496668 CHVBK 20210128105157.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10231-013-0387-x doi (NATIONALLICENCE)springer-10.1007/s10231-013-0387-x Spaces of bounded spherical functions on Heisenberg groups: part II [Elektronische Daten] [Chal Benson, Gail Ratcliff] Consider a linear multiplicity free action by a compact Lie group $$K$$ K on a finite dimensional Hermitian vector space $$V$$ V . Letting $$K$$ K act on the Heisenberg group $$H_V=V\times \mathbb {R}$$ H V = V × R yields a Gelfand pair. The condition that $$K:V$$ K : V be "well-behaved” establishes a relationship between the associated moment mapping and highest weight vectors occurring in the polynomial ring $${\mathbb {C}}[V]$$ C [ V ] . Under this condition, an application of the Orbit Method produces a topological embedding of the space of bounded spherical functions for $$(K,H_V)$$ ( K , H V ) in the space of $$K$$ K -orbits in the dual of the Lie algebra for $$H_V$$ H V . In part I of this work, it was shown that every irreducible multiplicity free action is well-behaved. Here we extend this result to encompass all multiplicity free actions. Our proof uses case-by-case analysis of multiplicity free actions which are indecomposable but not irreducible. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Gelfand pairs nationallicence Spherical functions nationallicence Nilpotent Lie groups nationallicence Orbit method nationallicence Benson Chal Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA aut Ratcliff Gail Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/2(2015-04-01), 533-561 0373-3114 194:2<533 2015 194 10231 https://doi.org/10.1007/s10231-013-0387-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0387-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Benson Chal Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA aut NATIONALLICENCE 700 1- Ratcliff Gail Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/2(2015-04-01), 533-561 0373-3114 194:2<533 2015 194 10231 SWISSBIB 605496609