Crystal Bases 1st Edition by Daniel Bump, Anne Schilling 9789814733441 981473344X

Crystal Bases 1st Edition by Daniel Bump, Anne Schilling  – Ebook PDF Instant Download/Delivery: 9789814733441, 981473344X
Full download Crystal Bases 1st Edition  after payment

Product details:

ISBN 10: 981473344X
ISBN 13: 9789814733441 
Author: Daniel Bump, Anne Schilling

This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

Crystal Bases 1st Table of contents:

1. Introduction

2. Kashiwara Crystals
2.1 Root systems
2.2 Kashiwara crystals
2.3 Tensor products of crystals
2.4 The signature rule
2.5 Root strings
2.6 The character
2.7 Related crystals and twisting
2.8 Dynkin diagrams and Levi branching
Exercises

3. Crystals of Tableaux
3.1 Type A crystals of tableaux
3.2 An example
Exercises

4. Stembridge Crystals
4.1 Motivation and examples
4.2 Stembridge axioms
4.3 Stembridge crystals as a monoidal category
4.4 Properties of Stembridge crystals
Exercises

5. Virtual, Fundamental, and Normal Crystals
5.1 Embeddings of root systems
5.2 Virtual crystals
5.3 Properties of virtual crystals
5.4 Fundamental crystals
5.5 Adjoint crystals
5.6 Fundamental crystals: The exceptional cases
5.7 Normal crystals
5.8 Reducible Cartan types
5.9 Similarity of crystals
5.10 Levi branching of normal crystals
Exercises

6. Crystals of Tableaux II
6.1 Column reading in type A
6.2 Crystals of columns
6.3 Crystals of tableaux
6.3.1 Crystal of tableaux: Type Cr
6.3.2 Crystal of tableaux: Type Br
6.3.3 Crystal of tableaux: Type Dr
Exercises

7. Insertion Algorithms
7.1 The RSK algorithm
7.2 The dual RSK algorithm
7.3 Edelman–Greene insertion
Exercises

8. The Plactic Monoid
8.1 The definition of the plactic monoid
8.2 The plactic monoid and Knuth equivalence
8.3 Crystals and Schensted insertion
8.4 Crystals of skew tableaux
Exercises

9. Bicrystals and the Littlewood–Richardson Rule
9.1 The GL(n) × GL(r) bicrystal
9.2 The crystal see-saw and the Littlewood–Richardson rule
Exercise

10. Crystals for Stanley Symmetric Functions
10.1 Stanley symmetric functions
10.2 Crystal on decreasing factorizations
10.3 Applications
Exercises

11. Patterns and the Weyl Group Action
11.1 String patterns
11.2 Gelfand–Tsetlin patterns
11.3 The Weyl group action
Exercises

People also search for Crystal Bases 1st :

    
warhammer crystal bases
    
necron crystal bases
    
introduction to quantum groups and crystal bases
    
40k crystal bases
    
wholesale crystal bases award

Tags:

Daniel Bump,Anne Schilling,Crystal Bases