Lie Groups (2nd Edition) (Graduate Texts in Mathematics, Volume 225)
By Daniel Bump
This publication is meant for a one-year graduate direction on Lie teams and Lie algebras. The e-book is going past the illustration concept of compact Lie teams, that is the foundation of many texts, and gives a delicately selected diversity of fabric to offer the coed the larger photo. The e-book is prepared to permit diversified paths in the course of the fabric looking on one's pursuits. This moment variation has mammoth new fabric, together with enhanced discussions of underlying ideas, streamlining of a few proofs, and plenty of effects and subject matters that weren't within the first edition.
For compact Lie teams, the ebook covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl staff, roots and weights, Weyl personality formulation, the basic crew and extra. The booklet maintains with the research of advanced analytic teams and basic noncompact Lie teams, protecting the Bruhat decomposition, Coxeter teams, flag types, symmetric areas, Satake diagrams, embeddings of Lie teams and spin. different themes which are handled are symmetric functionality thought, the illustration concept of the symmetric crew, Frobenius–Schur duality and GL(n) × GL(m) duality with many purposes together with a few in random matrix thought, branching principles, 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 using Sage mathematical software program for Lie crew computations.