#GRATUIT PDF ½ Lie Groups Í eBook or E-pub free

#FREE PDF õ Lie Groups Î From the reviews of the second editionThe book begins with a detailed explanation of the basic facts It contains a discussion of very nontrivial modern applications of Lie group theory in other areas of mathematics The text is very interesting and is superior to other textbooks on Lie group theory Dmitri Artamonov, zbMATH, Vol , This second edition of a successful graduate textbook and reference is now divided in four parts the book under review is the one every one of us must have on its desk or night table this is a well organized book with clear and well established goals, taking the interested reader to the frontiers of today s research Felipe Zaldivar, MAA Reviews, December,This book is intended for a one year graduate course on Lie groups and Lie algebras The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture The book is organized to allow different paths through the material depending on one s interests This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first editionFor compact Lie groups, the book covers the Peter Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group andThe book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius Schur duality and GL n GL m duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and the cohomology of Grassmannians An appendix introduces the reader to the use of Sage mathematical software for Lie group computations