| Description |
1 online resource (vii, 320 pages) |
| Series |
Cambridge tracts in mathematics ; 199 |
|
Cambridge tracts in mathematics ; 199.
|
| Contents |
Introduction -- 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 |
| Summary |
"Highest weight modules play a key role in the representation theory of several classes of algebraic objects occurring in Lie theory, including Lie algebras, Lie groups, algebraic groups, Chevalley groups and quantized enveloping algebras. In many of the most important situations, the weights may be regarded as points in Euclidean space, and there is a finite group (called a Weyl group) that acts on the set of weights by linear transformations. The minuscule representations are those for which the Weyl group acts transitively on the weights, and the highest weight of such a representation is called a minuscule weight"-- Provided by publisher |
|
Uses the combinatorics and representation theory to construct and study important families of Lie algebras and Weyl groups |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Representations of Lie algebras.
|
|
Combinatorial analysis.
|
|
MATHEMATICS -- Algebra -- General.
|
|
MATHEMATICS -- Algebra -- Intermediate.
|
|
Análisis combinatorio
|
|
Lie, Áglebras de
|
|
Combinatorial analysis
|
|
Representations of Lie algebras
|
| Form |
Electronic book
|
| ISBN |
9781107308893 |
|
1107308895 |
|
9781107314443 |
|
1107314445 |
|
9781139207003 |
|
1139207008 |
|
9781299009066 |
|
1299009069 |
|
9781107306691 |
|
1107306698 |
|
9781107301603 |
|
1107301602 |
|
1107236525 |
|
9781107236523 |
|
1107305764 |
|
9781107305762 |
|
1107312248 |
|
9781107312241 |
|
