Lie theory : Lie algebras and representations
著者
書誌事項
Lie theory : Lie algebras and representations
（Progress in mathematics, v. 228）
Birkhäuser, c2004
- : us
- : sz
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注記
Includes bibliographical references
収録内容
- Nilpotent orbits in representation theory / Jens Carsten Jantzen
- Infinite-dimensional groups and their representations / Karl-Hermann Neeb
内容説明・目次
内容説明
* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians.
* Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations."
* Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations.
* Should benefit graduate students and researchers in mathematics and mathematical physics.
目次
Preface * J.C. Jantzen, 'Nilpotent Orbits in Representation Theory': * Introduction * Nilpotent Orbits for Classical Groups * Some General Results * Centralisers in the Classical Cases * Bala-Carter Theory * Centralisers * The Nilpotent Cone I * The Nilpotent Cone II * Functions on Orbits and Orbit Closures * Associated Varieties * Springer's Fibres and Steinberg's Triples * Paving Springer's Fibres * l-adic and Perverse Stuff * Springer's Representations * References * K.-H. Neeb, 'Infinite Dimensional Groups and their Representations': * Introduction * The Finite-Dimensional Case * Split Lie Algebras * Unitary Highest Weight Modules * Banach-Lie Groups * Holomorphic Representations of Classical Banach-Lie Groups * Geometry of Coadjoint Orbits of Banach-Lie Groups * Coadjoint Orbits and Complex Line Bundles for U2(H) * Appendix: The Topology of Classical Banach-Lie Groups * References
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