A proof of the polynomial conjecture for nilpotent Lie groups monomial representations

DOI10.1090/tran/8855WikidataQ123166404 ScholiaQ123166404MaRDI QIDQ6135824

Hidenori Fujiwara, Ali Baklouti, Jean Ludwig

Publication date: 28 August 2023

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

differential operatorsorbit methodmonomial representations

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) (22E27)

Cites Work

• Analyse harmonique sur les espaces symétriques nilpotents
• Représentations monomiales des groupes de Lie nilpotents. (Monomial representations of nilpotent Lie groups)
• Harmonic analysis of some induced representations of a nilpotent Lie group
• Abstract Plancherel theorems and a Frobenius reciprocity theorem
• A commutativity criterion for certain algebras of invariant differential operators on nilpotent homogeneous spaces
• Harmonic analysis on differential operators on nilpotent homogeneous spaces.
• Spectral decomposition of invariant differential operators on certain nilpotent homogeneous spaces
• On \(C^\infty\)-vectors and intertwining bilinear forms for representations of Lie groups
• Direct Integral Decompositions and Multiplicities for Induced Representations of Nilpotent Lie Groups
• Commutativity of invariant differential operators on nilpotent homogeneous spaces with finite multiplicity
• Orbital Parameters for Induced and Restricted Representations
• Representation Theory of Solvable Lie Groups and Related Topics
• A proof of the polynomial conjecture for restrictions of nilpotent lie groups representations
• Invariant differential operators on certain nilpotent homogeneous spaces
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