By Daniel Bump
This ebook is meant for a one-year graduate direction on Lie teams and Lie algebras. The booklet is going past the illustration conception of compact Lie teams, that's the foundation of many texts, and gives a gently selected diversity of fabric to provide the coed the larger photograph. The e-book is equipped to permit assorted paths throughout the fabric counting on one's pursuits. This moment variation has giant new fabric, together with superior 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 e-book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl workforce, roots and weights, Weyl personality formulation, the elemental staff and extra. The booklet maintains with the learn of complicated analytic teams and basic noncompact Lie teams, overlaying the Bruhat decomposition, Coxeter teams, flag kinds, symmetric areas, Satake diagrams, embeddings of Lie teams and spin. different issues which are taken care of are symmetric functionality thought, the illustration thought of the symmetric workforce, Frobenius–Schur duality and GL(n) × GL(m) duality with many functions together with a few in random matrix conception, 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 workforce computations.