Introduction to Quantum Groups

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