This booklet 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's the foundation of many texts, and offers a delicately selected variety of fabric to provide the scholar the larger photograph. The e-book is geared up to permit diversified paths during the fabric counting on one's interests. This moment version has large new fabric, together with greater discussions of underlying rules, streamlining of a few proofs, and plenty of effects and themes 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 workforce, roots and weights, Weyl personality formulation, the elemental team and extra. The ebook maintains with the research of advanced analytic teams and common noncompact Lie teams, masking the Bruhat decomposition, Coxeter teams, flag types, symmetric areas, Satake diagrams, embeddings of Lie teams and spin. different themes which are taken care of are symmetric functionality concept, the illustration concept of the symmetric workforce, Frobenius–Schur duality and GL(n) × GL(m) duality with many purposes together with a few in random matrix conception, branching principles, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp varieties" and the cohomology of Grassmannians. An appendix introduces the reader to using Sage mathematical software program for Lie team computations.