178 INDEX O F NOTATIO N
S
M
Th e Young subgrou p S
M l
x 6
M 2
x 2 8
#?(&„) Th e Iwahori-Heck e algebr a o f 6
M
2 8
M^ Th e "permutatio n module " m ^ 2 8
^M Distinguishe d cose t representative s o f 6
M
2 9
d(t) Th e elemen t o f 6
n
suc h tha t t = t^d(t ) 2 9
, Th e dominanc e orde r 3 0
t jra Th e subtablea u o f t containing 1, 2,..., m 3 0
3.2 * Th e ^-linea r antiautomorphis m o f J4? 3 2
determined by T^ = T
w
-i fo r al l it; G S
n
rd%)mMTd(t) 3 2
M Th e Murph y basi s {ra
st
} o f J f 3 4
A+ Th e se t o f partitions o f n ordere d b y dominanc e 3 5
J^x
Th e idea l of Jff wit h basi s th e se t o f ra
UD
where u 3 7
and t ) are standar d /i-tableau x wit h \x \ A
JfA
Th e idea l of Jf" wit h basi s th e se t o f ra
UD
wher e u 3 7
and t ) are standar d //-tableau x wit h \x A
SA
Th e Specht modul e indexe d b y A 3 8
rat A standar d basi s elemen t o f a Spech t modul e 3 8
Dx A simple JT-module ; £ A = S x/radSx 3 8
3.3 L
fc
g- 12 T
( f c
_
12
^
)
+g- L
( f c
_
5 f c )
+ .. . +
9
1-/cT(1,fc) 3 9
[m]q Th e 'quantum integer ' 1 -f- g -j- -f q 171 "1 4 1
[ra]g Th e 'quantum factorial ' [l]g[2]
q
... [ra]
g
4 1
e Th e smalles t positiv e intege r suc h tha t [e]
q
=0 4 1
res(x) Th e e-residu e o f x 4 1
ft A n orthogona l basi s elemen t o f S x 4 2
3.4 l
e
{hj) = j z + e( z 1), the ladder numbe r o f the node (i,j) 4 6
Mg [/^l]g[M2]g...[ ^ 4 6
A' Th e partition conjugat e t o A 4 9
Chapter 4 .
4.1 A(d,n ) {/iN= n |/ i = (/xi,...,/x
d
)} 5 5
y(d,n) Th e g-Schu r algebra ; als o S^R iq{d,n) 5 5
J^(n) «^(n,n ) ' 5 5
UJ Th e partitio n (l
n
) 5 6
S, T,... (Semistandard ) tableau x o f type /j, 5 6
7o(//, ^) Th e se t o f semistandard /i-tableau x o f type v 5 6
T
M
Th e uniqu e semistandar d /i-tablea u o f type / i 5 6
z/(t) Th e tablea u o f type i / obtained fro m t by replacing 5 6
each entr y i n t by it s ro w inde x i n i
v
fidDis Th e compositio n suc h tha t &^dnv = d
_ 1
6
M
d D 6^ 5 6
5 ^ Th e se t o f distinguished (6 M, 6^)-double cose t 5 7
representatives
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