Frobenius Reciprocity and Extensions of Nilpotent Lie Groups

DOI10.2307/2000612zbMath0606.22006OpenAlexW4236397976MaRDI QIDQ3744393

Jeffrey Fox

Publication date: 1986

Full work available at URL: https://doi.org/10.2307/2000612

zbMATH Keywords

solvable Lie groupsFrobenius reciprocityreduction theoremmultiplicity formuladiscrete cocompact subgroupquasi-regular representationsolvemanifold

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Nilpotent and solvable Lie groups (22E25)

Related Items (2)

On the Spectra of Compact Nilmanifolds ⋮ Height Zeta Functions of Equivariant Compactifications of Unipotent Groups

Cites Work

• 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
• Intertwining operators for representations induced from uniform subgroups
• On a connection between nilpotent groups and oscillatory integrals associated to singularities
• Topics in harmonic analysis on solvable algebraic groups
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Factor spaces of solvable groups
• Realization of Square-Integrable Representations of Unimodular Lie Groups on L 2 -Cohomology Spaces
• Lie Cohomology of Representations of Nilpotent Lie Groups and Holomorphically Induced Representations
• Decomposition of C ∞ Intertwining Operators for Lie Groups
• Spherical Distributions on Lie Groups and C ∞ Vectors
• Canonical Objects in Kirillov Theory on Nilpotent Lie Groups
• Unitary representations of solvable Lie groups
• On Frobenius Reciprocity for Unipotent Algebraic Groups Over Q
• The plancherel formula for group extensions
• Decomposition of the L 2 -Space of a General Compact Nilmanifold

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