Other available formats:
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact email@example.com providing details of the course you are teaching.
Minuscule representations occur in a variety of contexts in mathematics and physics. They are typically much easier to understand than representations in general, which means they give rise to relatively easy constructions of algebraic objects such as Lie algebras and Weyl groups. This book describes a combinatorial approach to minuscule representations of Lie algebras using the theory of heaps, which for most practical purposes can be thought of as certain labelled partially ordered sets. This leads to uniform constructions of (most) simple Lie algebras over the complex numbers and their associated Weyl groups, and provides a common framework for various applications. The topics studied include Chevalley bases, permutation groups, weight polytopes and finite geometries. Ideal as a reference, this book is also suitable for students with a background in linear and abstract algebra and topology. Each chapter concludes with historical notes, references to the literature and suggestions for further reading.Read more
- The author's example-driven combinatorial approach makes explicit calculations easy
- Discusses many applications in detail
- Includes numerous exercises and hints to solutions
Reviews & endorsements
"This monograph could be read with profit not only by the specialist, but also by an interested graduate student with some background on Lie algebras."
Felipe Zaldivar, MAA ReviewsSee more reviews
"The exposition [is] very clear. The book is strongly recommended to students and researchers who are interested in combinatorial aspects of representation theory."
Hiro-Fumi Yamada, Mathematical Reviews
"… useful as a book for students, the book under review is particularly useful as a reference for researchers of relevant fields."
Qendrim R. Gashi, Zentralblatt MATH
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: April 2013
- format: Hardback
- isbn: 9781107026247
- length: 330 pages
- dimensions: 231 x 155 x 23 mm
- weight: 0.61kg
- contains: 70 b/w illus. 7 tables 275 exercises
- availability: Available
Table of Contents
1. Classical Lie algebras and Weyl groups
2. Heaps over graphs
3. Weyl group actions
4. Lie theory
5. Minuscule representations
6. Full heaps over affine Dynkin diagrams
7. Chevalley bases
8. Combinatorics of Weyl groups
9. The 28 bitangents
10. Exceptional structures
11. Further topics
Appendix A. Posets, graphs and categories
Appendix B. Lie theoretic data
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×