Index
Chd(V ), 221
Fk, Fubini forms, 217
Flag1,2(V ), 164
Flatr, 178
G-invariants, 149
G-module, 30
G-module map, 138
G-variety, 110, 164
G(2,V ), equations for, 106
G(k, V ) Grassmannian, 106
G/P , 166
equations for, 169
GL(V ), 30
GLvC, 30
I(X), 99
J(Y, Z), join of varieties, 118
N(V ), 246
PD, 364
Rj
X
, 122
RankA,
r
178
SL(V ), 47
S2V , 40
Sd(A1⊗
· · · An), decomposition of, 149
SdV
, 42
as subspace of V ⊗d invariant under Sd,
48
STπ V , 144
SπV , 145
S21V , 54
STπ V , 144
SπV , 145, 184
SπV , 145
invariant definition of, 148
Seg(PA × PB), 102
Sflatr(SdV ∗), 178
Subr, 69
Subr(SdV
), 69
equations of, 176
Subr(SdV ), symmetric subspace variety,
176
Subr(ΛkV
), skew-symmetric subspace
variety, 177
Tx
∗X,
cotangent space, 113
TxX, intrinsic tangent space, 113
U(g), 386
U
⊥,
28
V/W , 111
V G, 149
V
⊗k,
33
Vˆ,
j
33
X-rank, 120
typical, 121
X∨, dual variety of X, 211
Xsing singular points of X, 107
Xsmooth, 107
[π]
definition, 143
[π], Sd-module, 141
C[G], group algebra of finite group, 139
C[V
]G,
246
C[X], 112
PV , 99
Sd, representations of, 140
Sn, 56
Λ2V
, 40
ΛkV , 44
Λg, 384
(
d
i1,...,iw
)
, 162
M1,2, 260
Q, 390
S, 175, 390
χV , character, 151
433
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