By Daniel Bump
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.
Read or Download Lie Groups: 225 (Graduate Texts in Mathematics) PDF
Best group theory books
Devoted to Anthony Joseph, this quantity includes surveys and invited articles by way of top experts in illustration idea. the focal point this is on semisimple Lie algebras and quantum teams, the place the influence of Joseph's paintings has been seminal and has replaced the face of the topic. introductory biographical overviews of Joseph's contributions in classical illustration idea (the idea of primitive beliefs in semisimple Lie algebras) and quantized illustration idea (the research of the quantized enveloping algebra) are by way of sixteen examine articles overlaying a few assorted and fascinating themes in illustration thought.
A very transformed re-creation of this terrific textbook. This key paintings is geared to the desires of the graduate scholar. It covers, with proofs, the standard significant branches of teams, jewelry, fields, and modules. Its inclusive technique implies that all the beneficial components are explored, whereas the extent of aspect is perfect for the meant readership.
Here's a key textual content with reference to illustration thought in finite teams. The pages of this wonderful little booklet, ready via Rafael Stekolshchik, include a couple of new proofs in terms of Coxeter alterations and the McKay Correspondence. They comprise rules and formulae from a couple of luminaries together with J.
The articles in those volumes arose from papers given on the 1991 overseas Symposium on Geometric crew concept, and so they characterize many of the most modern considering during this zone. this primary quantity includes contributions from some of the world's major figures during this box, and their contributions reveal the numerous fascinating points of geometrical crew concept.
- Pseudo-Differential Operators, Generalized Functions and Asymptotics: 231 (Operator Theory: Advances and Applications)
- Abelian Groups (Springer Monographs in Mathematics)
- Groups - St Andrews 1981 (London Mathematical Society Lecture Note Series)
- Models, Modules and Abelian Groups: In Memory of A. L. S. Corner
Extra info for Lie Groups: 225 (Graduate Texts in Mathematics)
Lie Groups: 225 (Graduate Texts in Mathematics) by Daniel Bump