International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.2, p. 67

## Section 1.2.7.4.2. Action of the generators of the point group G on the basis

M. Ephraïm,b T. Janssen,a A. Jannerc and A. Thiersd

#### 1.2.7.4.2. Action of the generators of the point group G on the basis

| top | pdf |

The transformation of the monomial under the matrix is given by the polynomial which is in principle non-commutative. This polynomial can be written as a sum of the monomials in the basis taking into account the eventual (anti)symmetry of and . In this way, basis element (a monomial) is transformed to To each generator of G corresponds such an action matrix M.

The action matrix changes if one considers pseudotensors. In the case of pseudotensors, the previous equation changes to The function Det(g) is just a one-dimensional representation of the group G. The determinant is either or .