Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups

DOI10.2307/2000731zbMath0629.22005OpenAlexW4248510752MaRDI QIDQ3765986

Gérard Grélaud, Frederick P. Greenleaf, Lawrence J. Corwin

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000731

zbMATH Keywords

multiplicityunitary representationnilpotent Lie groupcoadjoint orbitssemialgebraic setsdirect integral decompositioninduced representation

Mathematics Subject Classification ID

Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27) Induced representations for locally compact groups (22D30) Real algebraic and real-analytic geometry (14Pxx)

Related Items (22)

The up-down formula for nil-homogeneous spaces ⋮ Analysis of restrictions of unitary representations of a nilpotent Lie group ⋮ Orbital Parameters for Induced and Restricted Representations ⋮ Orbital decompositions of representations of non-simply connected nilpotent groups ⋮ Unnamed Item ⋮ Analysis of some monomial representations of exponential solvable Lie groups ⋮ Visible actions and criteria for multiplicity-freeness of representations of Heisenberg groups ⋮ A proof of the polynomial conjecture for restrictions of nilpotent lie groups representations ⋮ A restriction theorem for ideals in the Schwartz algebra of a nilpotent Lie group ⋮ Unnamed Item ⋮ A proof of the polynomial conjecture for nilpotent Lie groups monomial representations ⋮ The multiplicity function of mixed representations on completely solvable Lie groups ⋮ Spectre d'opérateurs de Schrödinger avec potentiel et champ magnetique polynomiaux. (Spectrum of Schrödinger operators where potential and magnetic field are polynomials) ⋮ On the isomorphism problem for C∗-algebras of nilpotent Lie groups ⋮ The Structure of the Space of Coadjoint Orbits of an Exponential Solvable Lie Group ⋮ Flat orbits, minimal ideals and spectral synthesis ⋮ A GENERALIZATION OF THE ORBIT METHOD ON A SIMPLY CONNECTED NILPOTENT LIE GROUP ⋮ Spectral decomposition of invariant differential operators on certain nilpotent homogeneous spaces ⋮ The Penney-Fujiwara Plancherel formula for Gelfand pairs ⋮ Complex Algebraic Geometry and Calculation of Multiplicities for Induced Representations of Nilpotent Lie Groups ⋮ The orbit method and Gelfand pairs, associated with nilpotent Lie groups ⋮ Unnamed Item

Cites Work

• Character formulas and spectra of compact nilmanifolds
• Representations of exponential Lie groups
• A new decision method for elementary algebra
• ASYMPTOTIC PROPERTIES OF POLYNOMIALS AND ALGEBRAIC FUNCTIONS OF SEVERAL VARIABLES
• A Representation-Theoretic Criterion for Local Solvability of Left Invariant Differential Operators on Nilpotent Lie Groups
• Unitary representations of solvable Lie groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups