Representations

Question 1

What is GL(V)

Answer 1

Question 2

What is a representation?

Answer 2

Question 3

What is the defining representation?

Answer 3

Question 4

What is the adjoint representation?

Answer 4

Question 5

What does it mean for a representation to be faithful?

Answer 5

Question 6

What does it mean for a subspace to be invariant?

Answer 6

Question 7

What does it mean for a representation to be irreducible?

Answer 7

Question 8

When is a representation unitary

Answer 8

Question 9

Give properties of the fundamental representation of SU(n)

Answer 9

Question 10

When can you decompose a representation

Answer 10

Question 11

When is there an invariant inner form on a compact lie group

Answer 11

Question 12

State Schur’s Lemma

Answer 12

Question 13

Describe the complex unitary representations of U(1)

Answer 13

Question 14

Define a Lie Algebra Homomorhpism

Answer 14

Question 15

Define a Lie Algebra representation

Answer 15

Question 16

Give the relationship between a lie group representation and a lie algebra representation

Answer 16

Question 17

Can we pick a hermitian basis of lie algebra representations

Answer 17

Question 18

What are the eigenvalues of p(sigma)

Answer 18

Question 19

What are the irreducible complex reps of SU(2)

Answer 19

Question 20

What are the reps of SO(3)

Answer 20