Kronecker products of projective representations of translation groups

Details Kronecker products of projective representations of translation groups Kronecker products of projective representations of translation groups

1997-09-23

arxiv.org/abs/cond-mat/9709251v1

5th WigSym, Kasperkovitz, Grau (eds) p.115, World Sci 1998

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

LaTeX 2.09, 7 pages, uses AMSSYM v2.2; presented as a poster at WigSym '97

Scientific paper

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'.

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