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