Lie Theory, 2004
Lie Algebras and Representations
Progress in Mathematics Series, Vol. 228

Coordinators: Anker Jean-Philippe, Orsted Bent

Language: English

158.24 €

Subject to availability at the publisher.

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Lie Theory
331 p. · 15.5x23.5 cm · Hardback

158.24 €

Subject to availability at the publisher.

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Lie Theory
331 p. · 15.5x23.5 cm · Paperback

Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title "Lie Theory," feature survey work and original results by well-established researchers in key areas of semisimple Lie theory.

A wide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, and harmonic analysis through a far-reaching generalization of Harish--Chandra's Plancherel formula for semisimple Lie groups. 

Ideal for graduate students and researchers, "Lie Theory" provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics.

Preface.- Nilpotent Orbits in Representation Theory.- 1 Nilpotent Orbits for Classical Groups.- 2 Some General Results.- 3 Centralizers in the Classical Cases.- 4 Bala-Carter Theory.- 5 Centralizers.- 6 The Nilpotent Cone I.- 7 The Nilpotent Cone II.- 8 Functions on Orbits and Orbit Closures.- 9 Associated Varieties.- 10 Springer’s Fibers and Steinberg’s Triples.- 11 Paving Springer’s Fibers.- 12 ?-adic and Perverse Stuff.- 13 Springer’s Representations.- References.- Infinite-Dimensional Groups and Their Representations.- I The Finite-Dimensional Case.- II Split Lie Algebras.- III Unitary Highest Weight Modules.- IV Banach-Lie Groups.- V Holomorphic Representations of Classical Banach-Lie Groups.- VI Geometry of Coadjoint Orbits of Banach-Lie Groups.- VII Coadjoint Orbits and Complex Line Bundles for U2(H).- Appendix: The Topology of Classical Banach-Lie Groups.- References.
Features 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/physics