量子群和晶体基引论(影印版) Jin,Hong，Seok-Jin Kang[著] 著 mobi 下载 网盘 caj lrf pdf txt 阿里云

“量子群”的概念是 V.G. Drinfel'd 和 M. Jimbo 在各自研究由二维可解格模型得到的量子Yang-Baxter方程时***引入的。量子群是Hopf代数的某些族，这些族是Kac-Moody代数的泛包络代数的变形。在过去的三十年中，它们已成为数学和数学物理的许多分支背后的基本代数结构，例如统计力学中的可解格模型，链环和结点的拓扑不变理论，Kac-Moody代数的表示论，代数结构的表示论，拓扑量子场论，几何表示论和C*-代数。

特别地，由 M. Kashiwara 和 G. Lusztig ***发展的“晶体基”或“典范基”理论为研究量子群的表示提供了一种强大的组合和几何工具。本书的目的是提供量子群和晶体基理论的基本介绍，重点放在理论的组合方面。

本书适合对非结合环和代数感兴趣的研究生阅读，也可供相关研究人员参考。

Introduction

Chapter 1. Lie Algebras and Hopf Algebras

1.1. Lie algebras

1.2. Representati*** of Lie algebras

1.3. The Lie algebra 8[(2, F)

1.4. The special linear Lie algebra [(n, F)

1.5. Hopf algebras

Exercises

Chapter 2. Kac-Moody Algebras

2.1. Kac-Moody algebras

2.2. Classification of generalized Cartan matrices

2.3. Representation theory of Kac-Moody algebras

2.4. The category Oint

Exercises

Chapter 3. Quantum Groups

3.1. Quantum groups

3.2. Representation theory of quantum groups

3.3. Al-forms

3.4. Classical limit

3.5. Complete reducibility of the category oiqt

Exercises

Chapter 4. Crystal Bases

4.1. Kashiwara operators

4.2. Crystal bases and crystal graphs

4.3. Crystal bases for Uq(12)-modules

4.4. Tensor product rule

4.5. Crystals

Exercises

Chapter 5. Existence and Uniqueness of Crystal Bases

5.1. Existence of crystal bases

5.2. Uniqueness of crystal bases

5.3. Kashiwara's grand-loop argument

Exercises

Chapter 6. Global Bases

6.1. Balanced triple

6.2. Global basis for V(A)

6.3. Polarization on Uq (g)

***. Triviality of vector bundles over p1

6.5. Existence of global bases

Exercises

Chapter 7. Young Tableaux and Crystals

7.1. The quantum group Uq(ln)

7.2. The category O>

7.3. Tableaux and crystals

7.4. Crystal graphs for Uq(gIn)-modules

Exercises

Chapter 8. Crystal Graphs for Classical Lie Algebras

8.1. Example: Uq(B3)-crystals

8.2. Realization of Uq(An-1)-crystals

8.3. Realization of Uq(Cn)-crystals

8.4. Realization of Uq(Bn)-crystals

8.5. Realization of Uq(Dn)-crystals

8.6. Tensor product decomposition of crystals

Exercises

Chapter 9. Solvable Lattice Models

9.1. The 6-vertex model

9.2. The quantum affine algebra Uq('[2)

9.3. Crystals and paths

Exercises

Chapter 10. Perfect Crystals

10.1. Quantum affine algebras

10.2. Energy functi*** and combinatorial R-matrices

10.3. Vertex operators for Uq([2)-modules

10.4. Vertex operators for quantum affine algebras

10.5. Perfect crystals

10.6. Path realization of crystal graphs

Exercises

Chapter 11. Combinatorics of Young Walls

11.1. Perfect crystals of level 1 and path realization

11.2. Combinatorics of Young walls

11.3. The crystal structure

11.4. Crystal graphs for basic representati***

Exercises

Bibliography

Index of symbols

Index

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