Index of notation
(- , - ) , (- , - }
r
, (- , -)Q,J, Euler form of
quiver, 49, 130, 131
(- , - ) , (- , ~)r , (- , ~)Q,T, symmetric
Euler form of quiver, 49, 130, 131
( ,—), Lusztig form on Green algebra, 524
(—)°, diamond functor, 425
(7, •), Cartan datum, 35, 523
(Q,cr), quiver with automorphism, 128
(W, *), Hecke monoid, 211
{W,S), Coxeter system, 184
(A,7,C,r), cellular datum, 720
(A,T,5), Specht datum, 719
[l,n] = { l , 2 , . . . , n } , 193
[M], isoclass of module M, 438
[n] = (vn - v~n)/(v - v-1), 20
[n]! = [l][2]...[n],20
[m]' symmetric Gaussian polynomial, 20
['Kt;a], Laurent polynomial in K over Q(v),
256, 309
[x;
t]1
= (x- l)(x -v)---(x- i ; *
- 1
) , 578
[n] = ( r - l ) / f o - l ) , 3 6
[n]' = [ n ] . [ n - l ] - - . [ l ] , 3 6
[^] , ordinary Gaussian polynomial, 18
|| ||, N-valued function on £(n), 559
| |: E(n) N, entry sum map, 371, 540
, RSK correspondence, 372
^ , Chevalley-Bruhat ordering, 192, 416,
558, 644
^ , partial ordering on weight lattice, 643
^dg degeneration ordering, 71
^L , ^ii , ^Lii) preorders defining left, right,
and two-sided cells, 335
=^, =^rc, partial orderings on S(n), 558
, dominance ordering, 395
^K i Knuth equivalence, 339
~v^5 Vogan equivalence, 342
U(n,r), set of symmetric matrices in
S(n,r), 418
V(A), costandard module, 426, 656, 708
A(A), standard module, 261, 293, 415, 658,
707
Av(f2), •u-exterior algebra, 14
JZ=Z[q], xxiii, 17
A n , affine n-space, 624
A(~\ Lie algebra obtained from an
associative algebra A, 7
= 0(Mn,v), 671
An,v(r), rth homogeneous component of
Xi,*, 672
An^v = (9(GLnjt;), An^v =
0(SLn,v), 678
A ^ = 0 ( M ^ ) , 6 8 3
An,v{r)- r ^h homogeneous component of
A % , 687
A(j) (A e S(ri)±, j G Z
n
) , basis element of
V, 598
2l(Q, r;g), Fg)Cr;g-fixed point algebra, 150
ad, adjoint representation, 8, 239, 283
Alg^, category of ^-algebras, 7
Alg^ , category of A-graded ^-algebras, 12
A-mod, category of finite dimensional left
A-modules, 83, 438, 699
A-mod F , category of finite dimensional
F-stable left A-modules, 92
£ ( ,—), bilinear form defined by a Coxeter
matrix, 185
749
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