Invariants and -spectrums of local theta lifts

DOI10.1112/S0010437X14007520zbMath1319.22009arXiv1302.1031OpenAlexW3106262297MaRDI QIDQ5179516

Jia-Jun Ma, Huang Yean Loke

Publication date: 20 March 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.1031

zbMATH Keywords

moment mapsnilpotent orbitsassociated varietieslocal theta liftsassociated cycles

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

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Cites Work

• A Mackey imprimitivity theory for algebraic groups
• Singular unitary representations of classical groups
• On the occurrence of admissible representations in the real Howe correspondence in stable range
• Modèles de Whittaker dégénéres pour des groupes p-adiques. (Degenerate Whittaker models of p-adic groups)
• Restrictions and expansions of holomorphic representations
• The closure of nilpotent orbits in the classical symmetric pairs and their singularities
• On the Segal-Shale-Weil representations and harmonic polynomials
• Characters, dual pairs, and unitary representations
• Dual pairs and Kostant-Sekiguchi correspondence. I
• Theta lifting of unitary lowest weight modules and their associated cycles
• On the geometry of conjugacy classes in classical groups
• Dual pairs and Kostant-Sekiguchi correspondence. II: Classification of nilpotent elements
• Local theta lifting of generalized Whittaker models associated to nilpotent orbits
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Troisième partie). Rédigé avec la colloboration de J. Dieudonné
• Structure of representations generated by vectors of highest weight
• On the quantization of spherical nilpotent orbits
• Theta lifting of nilpotent orbits for symmetric pairs
• Lie Group Representations on Polynomial Rings
• Howe quotients of unitary characters and unitary lowest weight modules