Nilpotent orbits and complex dual pairs

DOI10.1006/jabr.1996.6910zbMath0870.22007OpenAlexW1991868335MaRDI QIDQ1355616

Witold Kraśkiewicz, Andrzej Daszkiewicz

Publication date: 19 August 1997

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f13c515b98802f487f81f1d178a78f429366c732

zbMATH Keywords

symplectic grouprepresentationsLie algebrasmoment mapnilpotent orbitcomplex symplectic vector spaceHowe's correspondencecomplex reductive dual pair

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46)

Related Items

Characters of irreducible unitary representations of 𝑈(𝑛,𝑛+1) via double lifting from 𝑈(1), Manifestly covariant worldline actions from coadjoint orbits. I: Generalities and vectorial descriptions, Theta correspondence and the orbit method, Howe correspondence and Springer correspondence for real reductive dual pairs, Compositions of theta correspondences, Dual pairs and Kostant-Sekiguchi correspondence. II: Classification of nilpotent elements, Theta lifting of nilpotent orbits for symmetric pairs, Nilpotent orbits of \(\mathbb Z_4\)-graded Lie algebra and geometry of moment maps associated to the dual pair \((U(p,q),U(r,s))\), Dual pairs and Kostant-Sekiguchi correspondence. I, THETA CORRESPONDENCE I — SEMISTABLE RANGE: CONSTRUCTION AND IRREDUCIBILITY

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