Index
above, 85
addable i-node, 76
adjoint representation, 2
affine Hecke algebra, 105
aperiodic, 139
bar involution, 47
bar involution of V (λ), 74
below, 85
Bernstein presentation, 106
canonical basis, 48
Cartan matrix, 17
Cartan subalgebra, 9
Casimir element of Uv(sl2), 25
Casimir operator, 40
coproduct, 6
crystal basis, 27, 46
crystal graph, 27
cyclic quiver, 123
decomposition number, 115
definition by generators and relations, 4
dimension vector, 123
dominance ordering, 113
dominant weight, 40
enveloping algebra, 3
free Lie algebra, 15
fundamental weight, 40
G-equivariant sheaf, 134
Hecke algebra, 97
highest weight module, 40
highest weight vector, 40
ideal of a Lie algebra, 2
i-good, 87
i-induction, 100, 118
i-normal, 87
integrable Uv-module, 23
integral multisegment, 141
intersection cohomology complex, 134
i-restriction, 100, 119
Jacobi identity, 2
Kac-Moody Lie algebra, 18
Kashiwara algebra, 42
Kashiwara operator, 27, 46
Kleshchev multipartition, 94
Kostant-Lusztig form, 47
ladder, 98
length, 105
Lie algebra, 2
Lie algebra defined by generators and rela-
tions, 16
Lie algebra homomorphism, 2
Lie group, 1
Lie subalgebra, 2
LLT conjecture, 97
modular system with parameters, 111
Morita equivalence, 117
multipartition, 85
multisegment, 125
node, 75
partition, 75
perverse sheaf, 134
primitive vector, 40
progenerator, 117
pullback, 127
pushforward, 127
quantum algebra of type Ar−1, 13
quantum algebra of type
A(1)
r−1
, 21
quantum Casimir operator, 40
realization of a Cartan matrix, 17
reduced expression, 105
removable i-node, 76
representations of a Lie group, 1
representation of a Lie algebra, 2
representation of a quiver, 123
residue of a segment, 125
Ringel-Hall algebra, 133
root, 9, 18
root space decomposition, 9, 18
root space decomposition of Uv, 39
root system, 9
r-residue, 75, 85
r-restricted, 98
157
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