INDEX O F NOTATIO N 179
first(T)
last(T)
Mu*
mst
mST
A+(d,n)
/?ST
^o(A)
yx(d,n)
yx(d,n)
*
wx
raT
(pT
Lx
first (T) t wheneve r u(t) = T
t last(T ) wheneve r u(t) = T
(MUY
=3tfm
v
YJB
m
s t wher e /x(s ) = S
S
s
t
m5t
wher e /i(s ) = S an d i/(t ) = T
The se t o f partition s i n A(d , n )
A semistandar d basi s elemen t
U
M
GA(d,n)
T
0(
A
^)
The idea l o f y{d,n) wit h basi s th e ^ ST
where S, T ar e i n %(a) an d a A
The idea l o f 5?{d,n) wit h basi s th e ^
ST
where S , T are i n To (a) an d a A
The automorphis m o f y(d,n) wit h £g
T
= ip
TS
The Wey l modul e indexe d b y A
J2t
m
t wher e /i(t ) = T
A semistandar d basi s elemen t o f W
x
The simpl e ^ - m o d u l e W
x/mdWx
57
58
59
59
60
61
61
61
61
61
61
62
62
62
63
Chapter 5 .
wx
4
K
[resT(fc)]g
7 T ( ? )
9XAQ)
a,/?
dT(a)
PC
n
hx
nab
JX
lab
Vp
w¥a

w*{i)
vv
"e,p{k)
(5A)°
The /x-weigh t spac e o f W
x
The Gra m determinan t o f W
x
A Jucys-Murph y elemen t o f E n d ^ ( M
M
)
Ex:T(x) = fc[
re8Wl?
A rationa l functio n
Another rationa l functio n
IIT7T(Z)
Sequences o f integer s (bet a numbers )
± di m W" wher e v i s determine d b y a
A sequenc e o f bet a number s
{ 1 , 2 , . . . , n }
The lengt h o f th e (a , b)
th
hoo k i n [A ]
The le g lengt h o f th e (a ,
b)th
hoo k i n A
The p-adi c valuatio n map , p a prim e
The virtua l Wey l modul e correspondin g t o a
The virtua l Spech t modul e correspondin g t o a
The i
th
modul e i n th e Jantze n filtratio n o f W
¥
The p-adi c valuation , fo r p a prim e intege r
vp(k) i f e|fc ; 1 otherwise .
The dua l o f S
x
69
69
69
70
71
73
75
76
76
76
76
79
79
81
82
82
83
88
89
89
Chapter 6 .
6.1 j€n Jt?(& n) 9 6
Res Th e restrictio n functo r fro m Jff
n
to c^_ i 9 6
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