Kronecker products of projective representations of translation groups
Wojciech Florek
Abstract
Projective irreps of (ZN)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'.
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