Lie Theory

"The references in this volume are extensive (especially for positive characteristic results) and include literature as recent as 2002. Some of Jantzen's techniques seem to be unmotivated at first, but he rewards the patient reader with background and motivation as he moves through the book, often starting with a simple case in a classical group/algebra and providing motivation by generalizing the situation later. The detailed work is also surprisingly free of logical and typographical errors; Jantzen has been very careful at every turn. ... ...Neeb's article is a good starting point for learning about the analytic side of the unitary representation theory of infinite-dimensional groups." -SIAM Book Reviews "This is the first volume in a series of three on the theory of semisimple Lie groups. It consists of two independent articles, which both are devoted to realtions between representation theory and adjoint or coadjoint orbits." ---Monatshefte fur Mathematik

• 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.