On the Spectra of Compact Nilmanifolds

DOI10.2307/2000299zbMath0583.22006OpenAlexW4229979892MaRDI QIDQ3708221

Jeffrey Fox

Publication date: 1985

Full work available at URL: https://doi.org/10.2307/2000299

zbMATH Keywords

Selberg trace formulaFrobenius reciprocitycompact nilmanifoldsconnected nilpotent Lie grouplattice subgroupsHowe-Richardson formulamultiplicity of representations

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Discrete subgroups of Lie groups (22E40) Nilpotent and solvable Lie groups (22E25) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Induced representations for locally compact groups (22D30)

Related Items (2)

Harmonic analysis on two and three-step nilmanifolds ⋮ Decomposition of quasi-regular representations induced from discrete subgroups of nilpotent Lie groups

Cites Work

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• Abstract Plancherel theorems and a Frobenius reciprocity theorem
• Character formulas and spectra of compact nilmanifolds
• A general character formula for irreducible projections on \(L^2\) of a nilmanifold
• Decomposition of unitary representations defined by discrete subgroups of nilpotent groups
• Frobenius Reciprocity and Extensions of Nilpotent Lie Groups
• On Frobenius Reciprocity for Unipotent Algebraic Groups Over Q
• Decomposition of the L 2 -Space of a General Compact Nilmanifold

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