Kronecker products of projective representations of translation groups
Abstract
Projective irreps of (Z_N)^2 can be labelled by divisors n of N. A product of two irreps, labelled by n and n', can be decomposed into projective irreps labelled by M, where M strongly depends on the arithmetic structure of N, n, n' and their relations (gcd, lcm etc.). Such decompostion describes two important physical effects: (i) changes of a magnetic period of the crystal lattice (with unchaged crystal period N); (2) each representation can be related with a charged particle moving in an external magnetic field and a periodic potential --- a product of (projective) irreps corresponds to interaction of particles with charges Q and Q', respectively, and the decomposition corresponds to a particle with the charg Q''=Q+Q'.
Keywords
Cite
@article{arxiv.cond-mat/9709251,
title = {Kronecker products of projective representations of translation groups},
author = {Wojciech Florek},
journal= {arXiv preprint arXiv:cond-mat/9709251},
year = {2008}
}
Comments
LaTeX 2.09, 7 pages, uses AMSSYM v2.2; presented as a poster at WigSym '97