Contents
Preface i x
Introduction x i
Symmetric function s x i
Schur function s an d thei r generalization s x i
Jacobi polynomial s attache d t o roo t system s xii i
Constant ter m identitie s xii i
References x v
Chapter 1. Symmetri c Function s 1
1. Th e rin g o f symmetric function s 1
2. Monomia l symmetri c function s 2
3. Elementar y symmetri c function s 3
4. Complet e symmetri c function s 3
5. Powe r sum s 4
6. Scala r produc t 5
7. Schu r function s 7
8. Zona l polynomial s 10
9. Jack' s symmetri c function s 1
10. Hall-Littlewoo d symmetri c function s 1
11. Th e symmetri c function s P A {Q,t) 12
12. Furthe r propertie s o f the P\ (q,t) 18
Chapter 2 . Orthogona l Polynomial s 2 3
1. Introductio n 2 3
2. Roo t system s 2 3
3. Orbi t sum s an d Wey l character s 2 5
4. Scala r produc t 2 6
5. Th e polynomial s P\ 2 7
6. Proo f o f the existenc e theore m 2 8
7. Proo f o f the existenc e theorem , conclude d 3 2
8. Som e propertie s o f the P\ 3 6
9. Th e genera l cas e 3 7
Chapter 3 . Postscrip t 3 9
1. Th e affin e roo t syste m an d th e extende d affin e Wey l grou p 3 9
2. Th e brai d grou p 4 0
3. Th e affin e Heck e algebra 4
4. Cherednik' s scala r produc t 4 3
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