The orbit method and Gelfand pairs, associated with nilpotent Lie groups

DOI10.1007/BF02921973zbMath0998.22002OpenAlexW2039206556WikidataQ115391141 ScholiaQ115391141MaRDI QIDQ1589362

Gail Ratcliff, Chal Benson, J. W. Jenkins

Publication date: 11 December 2000

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921973

zbMATH Keywords

nilpotent Lie groupcoadjoint orbitsGelfand paircompact Lie group

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Summability methods on groups, semigroups, etc. (43A55)

Related Items (16)

Weak symmetry in naturally reductive homogeneous nilmanifolds ⋮ Some harmonic analysis on commutative nilmanifolds ⋮ Unnamed Item ⋮ Corwin–Greenleaf multiplicity function for compact extensions of the Heisenberg group ⋮ Unnamed Item ⋮ An orbit model for the spectra of nilpotent Gelfand pairs ⋮ The space of bounded spherical functions on the free 2-step nilpotent Lie group ⋮ Gelfand pairs attached to representations of compact Lie groups ⋮ A geometric criterion for Gelfand pairs associated with nilpotent Lie groups ⋮ Weakly symmetric pseudo-Riemannian nilmanifolds ⋮ Matrix spherical analysis on nilmanifolds ⋮ Modified \(H\)-type groups and symmetric-like Riemannian spaces ⋮ A generalized Gelfand pair attached to a 3-step nilpotent Lie group ⋮ Orbit method and dual topology for certain Lie groups ⋮ Generalized Gelfand pairs associated to \(m\)-step nilpotent Lie groups ⋮ Coherent states and Berezin quantization for non-scalar holomorphic representations

Cites Work

• Multiplicity-free spaces
• Spectrum and multiplicities for restrictions of unitary representations in nilpotent Lie groups
• Orbit theory and harmonic analysis on Lie groups with co-compact nilradical
• Some remarks on nilpotent orbits
• Projections of orbits and asymptotic behavior of multiplicities for compact connected Lie groups
• Geometric quantization and multiplicities of group representations
• A geometric criterion for Gelfand pairs associated with the Heisenberg group
• On Gelfand pairs associated with nilpotent Lie groups
• A classification of multiplicity free actions
• On Gelfand Pairs Associated with Solvable Lie Groups
• Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups
• Complex Algebraic Geometry and Calculation of Multiplicities for Induced Representations of Nilpotent Lie Groups
• The moment map for a multiplicity free action
• Orbital Parameters for Induced and Restricted Representations
• Restricting Representations of Completely Solvable Lie Groups
• Unnamed Item
• Unnamed Item
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