Index

This index contains mainly references to definitions and main results. In some

cases (such as "semisimplicity of [/-modules") you will be directed to subsections

containing results on the topic, but where the phrase from the index does not occur

explicitly in that form.

adjoint representation 4.18

admissible lattice

antipode

augmentation

braid group

braid relations

canonical basis

center of U

character formula

Clebsch-Gordan

formula

coassociative

cocommutative

comultiplication

counit

crystal base

crystal graph

divided powers

dominant short root

dual space of a

module

elementary move

fixed points

formal caharcters

fundamental weights

Gaussian binomial

coefficient

grading of U

Harish-Chandra

homomorphism

Hecke algebra

9.3

3.6/7, 3.8, 9.13

3.5

7.6, 8.15

7.6, 8.15

11.16

2.17, 2.10, 6.25

5.15

5A.8, 9.14

3.2

3.8

3.1/2, 3.8, 9.13

3.4/5, 3.8

9.4, 10.16

9.28

8.2, 8.6, 11.1

5A.2, 5A.9, 11.4

3.9, 5.3, 5.16

8.18

3.5

5A.8

4.1

0.1, 0.4, 8.1, 10.5

1.9, 4.7, 6.1

6.4, 6.6, 6.25

7.7

hexagon identities

Horn space of

modules

Hopf algebra

invariant form on U

isotypic component

Kostant's partition

function

largest short root

locally nilpotent

matrix coefficients

minuscule dominant

weights

modules of type 1

mod-Ti -invariant

pairing of U-° and

PBW type bases

polarization

quantized enveloping

algebra

3.18/19, 7.8

3.10, 5.3

3.8, 4.8, 4.11,

7.11

6.20

9.10

5.19

5A.2, 5A.9, 9.6,

9.21, 11.4

5.7

6.22, 7.10

5A.1, 5A.9, 9.6,

9.21 11.4

3.19', 5.2

9.20

6.12, 6.18,

8.28-30

1.5, 8.24

9.23, 10.16, 11.7

1.1, 4.3/4

quantum determinant 7.13

quantum trace

3.10, 5.3

quantum Yang-Baxter

equation

reduced expression

i?-matrices

3.17, 7.5/6

8.18

7.13, 8.30

265