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Littlewood-Richardson rule 20:09:33

Littlewood-Richardson rule 2 - example

Littlewood-Richardson rule 10:10:34

Littlewood-Richardson rule 1 - heuristics

Young diagrams and0:03:48

Young diagrams and irreps of O(N) and SO(N)

Young diagrams and0:04:09

Young diagrams and irreps of U(N) and SU(N)

GL(2) irrep carried0:09:46

GL(2) irrep carried by mixed rank 3 tensors in 2 dimensions

mixed rank 30:03:29

mixed rank 3 tensors in 2 dimensions

totally anti-symmetric tensors0:02:09

totally anti-symmetric tensors

totally symmetric tensors0:04:41

totally symmetric tensors

tensor products: irreducible0:05:39

tensor products: irreducible invariant subspaces w.r.t. Sₙ

permuting tensor indices0:03:14

permuting tensor indices

Cayley transform 10:05:10

Cayley transform 1 - unitary to Hermitian

a basis for0:02:24

a basis for the enveloping algebra

ad defines a0:05:01

ad defines a rep of the Lie algebra on the Lie algebra

U(n)=exp(iu(n))0:01:51

U(n)=exp(iu(n))

Cayley transform 20:02:17

Cayley transform 2 - inverse

irreps of SO(3)0:05:17

irreps of SO(3) from irreps of so(3)

J² and the0:02:18

J² and the ladder operators

ladder operators for0:03:30

ladder operators for so(3)

Casimir operator for0:04:43

Casimir operator for so(3)

rotations from the0:05:56

rotations from the so(3) Lie algebra

Haar measure 70:05:56

Haar measure 7 - right invariance and modular function

Haar measure 60:05:21

Haar measure 6 - proof of left invariance

Haar measure 50:06:20

Haar measure 5 - (local) change of coordinates

Haar measure 40:04:12

Haar measure 4 - calculation for Lie groups