V06·Act II · Space
How A5 splits the twelve-port space
The four symmetry blocks drawn as actual modes on the sphere. The 3-block is a dipole, the 5-block a quadrupole, because that is literally what they are.
The relation on screen
The port space carries a representation of A5, and it splits into irreducibles with no freedom left.
Symbols
- the two three-dimensional irreps of A5
- the five-dimensional irrep
diagonalising the carrier
what to look for · Blocks are exact. Nothing in this panel is fitted, and mixing between blocks is forbidden by Schur's lemma.
Consensus to physics
- 01the 12 ports carry a permutation action of A5
- 02that action splits the 12-dimensional signal space into irreducible blocks
- 03the decomposition is 1 + 3 + 5 + 3'
- 04repair, being A5-equivariant, cannot mix the blocks
In standard physics
Spherical harmonics and selection rules
The same argument that forbids transitions between angular-momentum sectors. The 3-block is an l=1 multiplet and the 5-block an l=2 multiplet, so the later dimension count follows from the carrier symmetry.
boundary · No dynamics yet. This is the decomposition that repair will act on; its result comes in V07.