vi CONTENTS
Chapter 10. The Hayashi realization 75
10.1. Partitions and the Hayashi realization 75
10.2. Generalization to the case of multipartitions 85
Chapter 11. Description of the crystal graph of V (Λ) 87
11.1. A theorem for proving the Misra-Miwa theorem 87
11.2. The Misra-Miwa theorem 94
Chapter 12. An overview of the applications to Hecke algebras 97
12.1. The Hecke algebra of type G(m, 1,n) 97
12.2. Consequences of Theorem 12.5 101
Chapter 13. The Hecke algebra of type G(m, 1,n) 105
13.1. The affine Hecke algebra 105
13.2. Semi-normal representations 107
13.3. The decomposition map 111
13.4. Specht module theory 113
13.5. A theorem of Morita type 117
13.6. Refined induction and restriction functors 118
Chapter 14. The proof of Theorem 12.5 123
14.1. Representations of a cyclic quiver 123
14.2. The Hall algebra and the quantum algebra 127
14.3. Some results from the geometric theory 133
14.4. Proof of the generalized LLT conjecture 142
Chapter 15. Reference guide 147
Bibliography 149
Index 157
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