[PDF] Representations And Nilpotent Orbits Of Lie Algebraic Systems eBook

Author : Maria Gorelik
Publisher : Springer Nature
Page : 553 pages
File Size : 33,63 MB
Release : 2019-10-18
Category : Mathematics
ISBN : 3030235319

GET BOOK

This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Author : William.M. McGovern
Publisher : Routledge
Page : 206 pages
File Size : 23,19 MB
Release : 2017-10-19
Category : Mathematics
ISBN : 1351428683

GET BOOK

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.

Author : Erhard Neher
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 45,45 MB
Release : 2011
Category : Mathematics
ISBN : 082185237X

GET BOOK

Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.

Author : Martin W. Liebeck
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 47,51 MB
Release : 2012-01-25
Category : Mathematics
ISBN : 0821869205

GET BOOK

This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.

Author : Niky Kamran
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 38,35 MB
Release : 1994
Category : Mathematics
ISBN : 0821851691

GET BOOK

This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 12,95 MB
Release : 2008-07-31
Category : Mathematics
ISBN : 0521889693

GET BOOK

This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.

Author : A. T. Fomenko
Publisher : CRC Press
Page : 316 pages
File Size : 45,20 MB
Release : 1988
Category : Mathematics
ISBN : 9782881241703

GET BOOK

Second volume in the series, translated from the Russian, sets out new regular methods for realizing Hamilton's canonical equations in Lie algebras and symmetric spaces. Begins by constructing the algebraic embeddings in Lie algebras of Hamiltonian systems, going on to present effective methods for constructing complete sets of functions in involution on orbits of coadjoint representations of Lie groups. Ends with the proof of the full integrability of a wide range of many- parameter families of Hamiltonian systems that allow algebraicization. Annotation copyrighted by Book News, Inc., Portland, OR