Group irreducible

Creation operator, 505 representation of, 507 Critical value, 338 Crystallographic point groups irreducible representations, 726 Crystallographic symmetry groups construction of mixed groups, 728 Crystal, eigenstates of, 725 Crystal symmetry, changes in, 758 Crystals... 

For the calculation of the g values only the latter second-order term and the first order spin term, which contain j3H, are significant, and in the former either OMg and nMg, or n Mg and 0 Ms must belong to the same double group irreducible representation for the contribution to be non-vanishing. 

A reducible representation is said to be the direct sum of the irreducible representations of which it is made up. In the standard notation (Section 9.5) for point-group irreducible representations, the 03v representation (9.29) is called A ( and the representation (9.28) is called E. If we denote the reducible representation (9.25) by T, then... 

Kovalev, O. V. (1993) Representations of the Crystallographic Space Groups Irreducible Representations, Induced Representations and Corepresentations, 2nd edn. Philadelphia, PA Gordon and Breach. 

These were assigned to the 2E(2Eg), Eb(2A2(2Tlg)), and (2A, Ea)(2Tlg) states (Figure 5.28) from the lower frequency side, where T denotes the double group irreducible representation.119,120 This assignment was based on the theoretical... 

We list in Table 8.45 the additional characters of the double group D3h and in Table 8.46 the y, M) basis functions for the double group irreducible representations of D3h-... 

Hermitian and unchanged by the operation. The notation used here conforms with the finite group irreducible tensor scheme 38, 39). We have already proved that cannot split the doublets and need therefore only discuss Now the states concerned are... 

This means that each state which is transformed according to the irreducible representation Au of the site group is split in the crystal into two exciton states of symmetry corresponding to the factor group irreducible representations Au and Bu, respectively. Sometimes such splitting is named a factor group splitting. 

The dimension of a space-group full representation (degeneracy of energy levels in a crystal) for a given k is equal to the product of the number of rays in the star k and the dimension of the point group irreducible representation (ordinary or projective). In particular, for the space group under consideration at the X point the dimensions of full representations are 6 and at the W point - 12. As to each of the... 

The decomposition (2.172) can be evaluated, as the direct product reduction to the group irreducible representations, from case to case, according to the procedure explained in above Section, yet the systematization mles with the aid of the decomposition rules in Table 2.11 help a lot. 

Table 1. Reduction of Space-group Irreducible Representations to the Cubic Site Group Irreducible Representations for the Face-Centered Cubic Lattice (for X and L Irreducible Representations only [25])...

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