Unitary group irreps

We assume that the canonical orbitals 95m (k,r) = (pbasis vectors of irrep 7 with wavevector k, n discriminates between the independent bases of equivalent irreps the index a replaces 7, m,ij, and s replaces a, k) of an energy band under consideration form a basis in the space < (q,/3) of some indrep of the group G > of a crystal. The localized functions are defined by a unitary transformation in the space of indrep ... 

It remains to discuss case 1, where both functions in a Kramers pair belong to the same irrep. For this case, ordinary point group symmetry does not promise any a priori blocking. We will therefore look for a unitary transformation on the Kramers pair basis that can block-diagonalize a matrix constructed over functions belonging to a case 1 irrep. The problem can be reduced to the diagonalization of a general 2x2 matrix spanned by the components of a Kramers pair. For the operator this is... 

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