Spaces of bounded spherical functions on Heisenberg groups: part I
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0377-z |2 doi |
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| 245 | 0 | 0 | |a Spaces of bounded spherical functions on Heisenberg groups: part I |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 associated Heisenberg group, $$H_V=V\times \mathbb{R }$$ H V = V × R yields a Gelfand pair. In previous work, we have applied the Orbit Method to produce an injective mapping $$\Psi $$ Ψ from the space $$\Delta (K,H_V)$$ Δ ( K , H V ) of bounded $$K$$ K -spherical functions on $$H_V$$ H V to the space $$\mathfrak{h }_V^*/K$$ h V ∗ / K of $$K$$ K -orbits in the dual of the Lie algebra for $$H_V$$ H V . We have shown that $$\Psi $$ Ψ is a homeomorphism onto its image provided that $$K:V$$ K : V is a "well-behaved” multiplicity free action. In this paper, we prove that $$K:V$$ K : V is well-behaved whenever $$K$$ K acts irreducibly on $$V$$ V . Thus, if $$K:V$$ K : V is an irreducible multiplicity free action then $$\Psi :\Delta (K,H_V)\rightarrow \mathfrak{h }_V^*/K$$ Ψ : Δ ( K , H V ) → h V ∗ / K is a homeomorphism onto its image. Our proof involves case-by-case analysis working from the classification of irreducible multiplicity free actions. A sequel to this paper will extend these results to encompass non-irreducible actions. | |
| 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 Multiplicity free actions |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), 321-342 |x 0373-3114 |q 194:2<321 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0377-z |q text/html |z Onlinezugriff via DOI |
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| 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/s10231-013-0377-z |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), 321-342 |x 0373-3114 |q 194:2<321 |1 2015 |2 194 |o 10231 | ||
| 986 | |a SWISSBIB |b 605496609 | ||