# symmetry.m

From Spinach Documentation Wiki

Permutation symmetry treatment. Compiles character tables of composite symmetry groups, builds the permutation table for each spin state in the basis, and builds projectors into the irreducible representations of the direct product symmetry group.

## Contents

## Syntax

spin_system=symmetry(spin_system,bas)

## Arguments

spin_system - Spinach spin system description object produced as described in the spin system and basis specification sections, of the of the online manual. bas - basis input structure described in the basis specification section of the manual

## Outputs

spin_system.bas.irrep(n).projector - projector matrices into each irreducible representation spin_system.bas.irrep(n).dimension - dimension of each ir- reducible representa- tion

## Notes

- This is a service function of the Spinach kernel that should not be called directly; it is called by basis.m
- Non-Abelian groups and multi-dimensional irreps are supported - edit perm_group.m to add your own groups.

## See also

reduce.m, perm_group.m, zte.m, basis.m

*Version 2.2, authors: Ilya Kuprov, Hannah Hogben*