nilpotent orbits primitive ideals and characteristic classes a geometric perspective in ring theory progress in mathematics

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Nilpotent Orbits Primitive Ideals And Characteristic Classes

Author : Walter Borho
ISBN : 9781461245582
Genre : Mathematics
File Size : 42. 3 MB
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1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.

Nilpotent Orbits In Semisimple Lie Algebra

Author : William.M. McGovern
ISBN : 9781351428682
Genre : Mathematics
File Size : 34. 41 MB
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Through the 1990s, a circle of ideas emerged relating three very different kinds of objects associated to a complex semisimple Lie algebra: nilpotent orbits, representations of a Weyl group, and primitive ideals in an enveloping algebra. The principal aim of this book is to collect together the important results concerning the classification and properties of nilpotent orbits, beginning from the common ground of basic structure theory. The techniques used are elementary and in the toolkit of any graduate student interested in the harmonic analysis of representation theory of Lie groups. The book develops the Dynkin-Konstant and Bala-Carter classifications of complex nilpotent orbits, derives the Lusztig-Spaltenstein theory of induction of nilpotent orbits, discusses basic topological questions, and classifies real nilpotent orbits. The classical algebras are emphasized throughout; here the theory can be simplified by using the combinatorics of partitions and tableaux. The authors conclude with a survey of advanced topics related to the above circle of ideas. This book is the product of a two-quarter course taught at the University of Washington.

Nilpotent Orbits In Semisimple Lie Algebra

Author : David .H. Collingwood
ISBN : 0534188346
Genre : Mathematics
File Size : 84. 8 MB
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Lie Theory

Author : Jens Carsten Jantzen
ISBN : 0817633731
Genre : Mathematics
File Size : 48. 39 MB
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* 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.

Mathematical Reviews

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ISBN : UOM:39015026169147
Genre : Mathematics
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Subject Guide To Books In Print

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ISBN : UOM:39015016312806
Genre : American literature
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Author : Archie Rugh
ISBN : 3598221312
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ISBN : STANFORD:36105025417838
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