Complete reduction bases for the principal induced representations of the crystallographic point groups

Abstract

An ordered partition P of a point group G is construc-

Quasiregular representations of space groups, application to the determination of symmetry change in phase transitions

“…Bases of the irreducible representations D, composing may be expressed in terms of linear combinations of the cosets H i , with complex coefficients (Masmoudi and Billiet, 1990). The basis G = cr='=l A,H (corresponding to po(r)) is a particular one, totally invariant by the elements of G. It spans the identity representation of G. po(r) is the totally symmetric part of p(r).…”

Representations of point groups spanned by sets of equivalent bipoints or multipoints

“…The concept of the principal induced representations (PIRs) of a crystallographic group has recently been a subject of increasing interest and several papers have been devoted to the properties and applications of PIRs (Litvin, 1982;Berenson, Kotzev & Litvin, 1982;Litvin, Kotzev & Birman, 1982;Masmoudi, 1990;Masmoudi & Billiet, 1989, 1990a. The PIRs of a group belong to a more extended category of representations designated as monomial representations (MRs).…”

“…For details of the well known mathematical definitions and properties mentioned in this paper, the reader is referred to the classic works (Gorenstein, 1968;Kirillov, 1976;Lomont, 1959;Malliavin, 1981;Murnagham, 1963;Serre, 1978). For other more specialized items and demonstrations, reference is made to Masmoudi (1990) and Masmoudi & Billiet (1989, 1990a.…”