Index o f notatio n
We us e standar d symbol s N , Z an d C fo r th e set s o f non-negativ e
integers, integer s an d comple x number s respectively ; i n addition , 6ij
is the Kronecke r delta .
Chapter 1.
1.1 &
n
Th e symmetri c grou p o n {1, 2,..., n} 1
Si Th e simpl e transpositio n (z, i +1) 1
S Th e Coxete r generator s {si,... , sn _i} o f &
n
1
£{w) Th e lengt h o f w G 6n 2
1.2 Jl? Th e Iwahori-Heck e algebr a o f 6
n
; als o ^
) g
( 6
n
) 5
T,, Ts Th e generator s r
x
,... , T
n
_
1
o f JT ' 5
Tw A basis elemen t o f Jff, t o G 6
n
5
Z Z[g,g _1an ], wher e q is indeterminat e ove r Z 8
^ 2 Th e generi c Iwahori-Heck e algebr a J%?z,q(&n) 8
Chapter 2 .
2.1 (A , ) Th e pose t indexin g th e cellula r basi s 16
T(A) A n indexin g se t fo r th e cellula r basi s 16
Ax Th e spa n o f the c^
d
wher e \i A 16
* Th e automorphis m o f A give n b y c
A
t
= c
A
5
16
,4A
Th e spa n o f the c^ wher e / i A 17
CA
A (right ) cel l modul e 17
C*A
A left cel l module 17
Dx C A /radC A 18
2.2 dx^ Th e compositio n multiplicit y o f D^ i n C
A
2 1
Chapter 3 .
3-1 \n\ EiM i 2 7
A N n A is a composition o f n 2 8
/i h n ^ x is a partition o f n 2 8
[/i] Th e diagra m { (z, j) \ 1 j fa an d z 1 } of \i 2 8
Shape(t) Th e shap e o f the tablea u t 2 8
s, t,... (Standard ) tableau x (o f type a; ) 2 8
Std(/i) Th e se t o f standard /i-tableau x 2 8
P Th e standar d /i-tablea u wit h 1, 2,..., n entere d 2 8
in order alon g it s rows .
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