Basics of groups and representations Flashcards
1
Q
Define a group
A
2
Q
Define conjugacy classes
A
3
Q
Define normal subgroup
A
4
Q
Define group homomorphism
A
5
Q
Give injectivity in terms of the kernel
A
6
Q
State FIT
A
7
Q
Define representation
A
8
Q
Define equivalence of representations
A
9
Q
Define unitary representations
A
10
Q
Define faithful representations
A
11
Q
Define reducible representation
A
12
Q
Define fully reducible
A
13
Q
Unitary reps are?
A
Unitary representations are fully reducible. Any representation of a finite group is unitary (relative to a suitable scalar
product) and, hence, fully reducible
14
Q
State Schur’s Lemma
A
15
Q
Define dual representation
A
16
Q
What is the Clebsch-Gordan decomposition
A
17
Q
What are the irreps of Zn
A
18
Q
Give useful kronecker product identities
A
