Spaces of bounded spherical functions on Heisenberg groups: part II
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0387-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0387-x | ||
| 245 | 0 | 0 | |a Spaces of bounded spherical functions on Heisenberg groups: part II |h [Elektronische Daten] |c [Chal Benson, Gail Ratcliff] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Gelfand pairs |2 nationallicence | |
| 690 | 7 | |a Spherical functions |2 nationallicence | |
| 690 | 7 | |a Nilpotent Lie groups |2 nationallicence | |
| 690 | 7 | |a Orbit method |2 nationallicence | |
| 700 | 1 | |a Benson |D Chal |u Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA |4 aut | |
| 700 | 1 | |a Ratcliff |D Gail |u Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 533-561 |x 0373-3114 |q 194:2<533 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0387-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0387-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Benson |D Chal |u Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ratcliff |D Gail |u Department of Mathematics, East Carolina University, 27858, Greenville, NC, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 533-561 |x 0373-3114 |q 194:2<533 |1 2015 |2 194 |o 10231 | ||
| 986 | |a SWISSBIB |b 605496609 | ||