Introduction to Quantum Groups

Authors:

ISBN: 978-0-8176-4716-2 (Print) 978-0-8176-4717-9 (Online)

Table of contents (42 chapters)

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  1. Front Matter

    Pages i-xiv

  2. THE DRINFELD JIMBO ALGERBRA U

    1. Front Matter

      Pages 1-1

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      Pages 2-13

      The Algebra f

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      Pages 14-18

      Weyl Group, Root Datum

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      Pages 19-33

      The Algebra U

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      Pages 34-39

      The Quasi- \(\mathcal{R}\) -Matrix

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      Pages 40-47

      The Symmetries \(T^{\prime}_{\rm {i, e}}, \ T^{\prime \prime}_{\rm {i, e}}\) of an Integrable U-Module

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      Pages 48-54

      Complete Reducibility Theorems

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      Pages 55-60

      Higher Order Quantum Serre Relations

  3. GEOMETRIC REALIZATION OF F

    1. Front Matter

      Pages 61-62

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      Pages 63-67

      Review of the Theory of Perverse Sheaves

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      Pages 68-80

      Quivers and Perverse Sheaves

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      Pages 81-88

      Fourier-Deligne Transform

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      Pages 89-91

      Periodic Functors

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      Pages 92-105

      Quivers with Automorphisms

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      Pages 106-112

      The Algebras \(\mathcal{O}^{\prime} {\rm k}\) and k

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      Pages 113-128

      The Signed Basis of f

  4. KASHIWARAS OPERATIONS AND APPLICATIONS

    1. Front Matter

      Pages 129-129

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      Pages 130-131

      The Algebra \(\mathfrak{U}\)

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      Pages 132-141

      Kashiwara’s Operators in Rank 1

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      Pages 142-151

      Applications

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      Pages 152-163

      Study of the Operators \(\tilde{F}_{i}, \ \tilde{E}_{i}\ {\rm on}\ {\Lambda}_{\lambda}\)

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      Pages 164-172

      Inner Product on \({\Lambda}\)

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      Pages 173-176

      Bases at ∞

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