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Introduction to Quantum Groups
Overview of attention for book
Table of Contents
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Book Overview
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Chapter 1
The Algebra f
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Chapter 2
Weyl Group, Root Datum
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Chapter 3
The Algebra U
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Chapter 4
The Quasi- $$\mathcal{R}$$ -Matrix
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Chapter 5
The Symmetries $$T^{\prime}_{\rm {i, e}}, \ T^{\prime \prime}_{\rm {i, e}}$$ of an Integrable U-Module
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Chapter 6
Complete Reducibility Theorems
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Chapter 7
Higher Order Quantum Serre Relations
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Chapter 8
Review of the Theory of Perverse Sheaves
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Chapter 9
Quivers and Perverse Sheaves
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Chapter 10
Fourier-Deligne Transform
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Chapter 11
Periodic Functors
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Chapter 12
Quivers with Automorphisms
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Chapter 13
The Algebras $$\mathcal{O}^{\prime} {\rm k}$$ and k
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Chapter 14
The Signed Basis of f
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Chapter 15
The Algebra $$\mathfrak{U}$$
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Chapter 16
Kashiwara’s Operators in Rank 1
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Chapter 17
Applications
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Chapter 18
Study of the Operators $$\tilde{F}_{i}, \ \tilde{E}_{i}\ {\rm on}\ {\Lambda}_{\lambda}$$
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Chapter 19
Inner Product on $${\Lambda}$$
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Chapter 20
Bases at ∞
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Chapter 21
Cartan Data of Finite Type
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Chapter 22
Positivity of the Action of F i , E i in the Simply-Laced Case
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Chapter 23
The Algebra $$\dot{\rm U}$$
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Chapter 24
Canonical Bases in Certain Tensor Products
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Chapter 25
The Canonical Basis $$\dot{\rm B} \ {\rm of} \ \dot{\rm U}$$
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Chapter 26
Inner Product on $$\dot{\rm U}$$
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Chapter 27
Based Modules
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Chapter 28
Bases for Coinvariants and Cyclic Permutations
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Chapter 29
A Refinement of the Peter-Weyl Theorem
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Chapter 30
The Canonical Topological Basis of $${\rm(U^{-} \ \bigotimes \ U^{+})}$$
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Chapter 31
The Algebra $$_R{\dot{\rm U}}$$
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Chapter 32
Commutativity Isomorphism
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Chapter 33
Relation with Kac-Moody Lie Algebras
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Chapter 34
Gaussian Binomial Coefficients at Roots of 1
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Chapter 35
The Quantum Frobenius Homomorphism
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Chapter 36
The Algebras $$R^{\mathfrak{f}}, \ R^{\mathfrak{u}}$$
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Chapter 37
The Symmetries $$T^{\prime}_{{i, e}}, \ T^{\prime \prime}_{{i, e}}$$ of U
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Chapter 38
Symmetries and Inner Product on f
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Chapter 39
Braid Group Relations
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Chapter 40
Symmetries and U +
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Chapter 41
Integrality Properties of the Symmetries
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Chapter 42
The ADE Case
Overall attention for this book and its chapters
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Book overview
1. The Algebra f
2. Weyl Group, Root Datum
3. The Algebra U
4. The Quasi- $$\mathcal{R}$$ -Matrix
5. The Symmetries $$T^{\prime}_{\rm {i, e}}, \ T^{\prime \prime}_{\rm {i, e}}$$ of an Integrable U-Module
6. Complete Reducibility Theorems
7. Higher Order Quantum Serre Relations
8. Review of the Theory of Perverse Sheaves
9. Quivers and Perverse Sheaves
10. Fourier-Deligne Transform
11. Periodic Functors
12. Quivers with Automorphisms
13. The Algebras $$\mathcal{O}^{\prime} {\rm k}$$ and k
14. The Signed Basis of f
15. The Algebra $$\mathfrak{U}$$
16. Kashiwara’s Operators in Rank 1
17. Applications
18. Study of the Operators $$\tilde{F}_{i}, \ \tilde{E}_{i}\ {\rm on}\ {\Lambda}_{\lambda}$$
19. Inner Product on $${\Lambda}$$
20. Bases at ∞
21. Cartan Data of Finite Type
22. Positivity of the Action of F i , E i in the Simply-Laced Case
23. The Algebra $$\dot{\rm U}$$
24. Canonical Bases in Certain Tensor Products
25. The Canonical Basis $$\dot{\rm B} \ {\rm of} \ \dot{\rm U}$$
26. Inner Product on $$\dot{\rm U}$$
27. Based Modules
28. Bases for Coinvariants and Cyclic Permutations
29. A Refinement of the Peter-Weyl Theorem
30. The Canonical Topological Basis of $${\rm(U^{-} \ \bigotimes \ U^{+})}$$
31. The Algebra $$_R{\dot{\rm U}}$$
32. Commutativity Isomorphism
33. Relation with Kac-Moody Lie Algebras
34. Gaussian Binomial Coefficients at Roots of 1
35. The Quantum Frobenius Homomorphism
36. The Algebras $$R^{\mathfrak{f}}, \ R^{\mathfrak{u}}$$
37. The Symmetries $$T^{\prime}_{{i, e}}, \ T^{\prime \prime}_{{i, e}}$$ of U
38. Symmetries and Inner Product on f
39. Braid Group Relations
40. Symmetries and U +
41. Integrality Properties of the Symmetries
42. The ADE Case
Summary
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