Contents
Introduction i x
Chapter 1. Th e Iwahori-Hecke algebr a of the symmetric group 1
1. Th e Symmetric group 1
2. Th e Iwahori-Hecke algebr a 5
3. Th e O-Hecke algebra 10
Chapter 2 . Cellula r algebra s 15
1. Cellula r bases 15
2. Simpl e modules in a cellular algebr a 19
Chapter 3 . Th e modular representatio n theor y of 3riP 2 7
1. Th e combinatorics of tableaux 2 7
2. Th e Murphy basis 3 2
3. Spech t module s and Jucys-Murph y element s 3 9
4. Irreducibl e ^-modules 4 5
Chapter 4 . Th e g-Schur algebr a 5 5
1. Semistandar d tableau x 5 5
2. A Specht filtratio n o f 5 9
3. Th e semistandard basi s theorem 6 1
Chapter 5 . Th e Jantzen su m formula an d the blocks of Jf? 6 9
1. Gra m determinants o f Weyl modules 6 9
2. Th e Jantzen su m formula 8 1
3. Th e blocks of y(n) an d 3ff 8 4
4. Irreducibl e Weyl modules and Spech t module s 8 7
Chapter 6 . Branchin g rules, canonical bases and decompositio n matrice s 9 5
1. Th e LLT algorithm 9 5
2. Decompositio n map s and adjustmen t matrice s 115
3. Th e Kleshchev-Brundan modula r branchin g rules 118
4. Rule s for computin g decomposition matrice s 122
5. Th e g-Schur algebra s and GL n(q) 129
6. Th e Ariki-Koike algebras and cyclotomic g-Schur algebra s 131
Appendix A. Finit e dimensional algebra s over a field 137
1. Filtration s an d composition serie s 137
2. Idempotent s an d indecomposable module s 138
3. Th e blocks of A 144
4. Semisimpl e symmetric algebra s 146
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