Algorithm for enumerating irreps

Irreps of crystallographic point groups or space groups are calculated in following steps:

Method-A (spgrep.irreps.enumerate_unitary_irreps_from_regular_representation())

1. Construct regular representation (crystallographic point group) or projective regular representation (space group).

2. Construct random matrix that commutes with (projective) regular representation and obtain irreps by diagonalizing it.

Method-B (spgrep.irreps.enumerate_unitary_irreps_from_solvable_group_chain())

1. Decompose little co-group \(\overline{\mathcal{G}}^{\mathbf{k}}\) into series

\[ 1 = G_{0} \triangleleft G_{1} \triangleleft \dots \triangleleft G_{m} = \overline{\mathcal{G}}^{\mathbf{k}}.\]

2. Construct irrep \(\Delta\) of \(G_{i}\) and use induced representation \(\Delta \uparrow G_{i+1}\) to obtain irreps of \(G_{i+1}\)

Subpages

• On-the-fly irreps generation from regular representation
• On-the-fly irreps generation from solvable group chain
• Intertwiner