Character formulas and spectra of compact nilmanifolds

DOI10.1016/0022-1236(76)90074-4zbMath0319.22011OpenAlexW1969103299MaRDI QIDQ1222737

Frederick P. Greenleaf, Lawrence J. Corwin

Publication date: 1976

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(76)90074-4

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Discrete subgroups of Lie groups (22E40) Nilpotent and solvable Lie groups (22E25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Analysis on other specific Lie groups (43A80)

Related Items

Cross-sections and an explicit formula for the Plancherel measure on a nilpotent Lie group, Criteria for Solvability of Left Invariant Operators on Nilpotent Lie Groups, Anosov actions of nilpotent Lie groups, Fourier transforms of smooth functions on certain nilpotent Lie groups, The non-existence of a non-abelian nilpotent Lie group with one discrete uniform subgroup up to automorphism, Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent Lie groups, Restrictions of irreducible unitary representations of nilpotent Lie groups to lattices, Harmonic analysis on two and three-step nilmanifolds, On approximation of Lie groups by discrete subgroups, On the Spectra of Compact Nilmanifolds, A class of idempotent measures on compact nilmanifolds, A general character formula for irreducible projections on \(L^2\) of a nilmanifold, The Plancherel measure in nilpotent Lie groups as a limit of point measures, Frobenius Reciprocity and Extensions of Nilpotent Lie Groups, Integral formulas with distribution kernels for irreducible projections in \(L^2\) of a nilmanifold, On the rational closure of connected closed subgroups of connected simply connected nilpotent Lie groups, Intertwining operators for representations induced from uniform subgroups, Poisson summation on Kirillov orbits, Spectra of compact quotients of the oscillator group, Height Zeta Functions of Equivariant Compactifications of Unipotent Groups, Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups, A Fourier transform for compact nilmanifolds with flat orbits, Order estimates for irreducible projections in \(L^ 2\) of a nilmanifold

Cites Work

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• Sur Les Représentations Unitaires Des Groupes De Lie Nilpotents. III
• Sur les Representations Unitaires des Groupes de Lie Nilpotents. IV
• Sur les représentations unitaires des groupes de Lie nilpotents. V
• On Frobenius Reciprocity for Unipotent Algebraic Groups Over Q
• Decomposition of the L 2 -Space of a General Compact Nilmanifold