A Matrix Model for νk1k2=(k1+k2)/k1k2Fractional Quantum Hall States

We have developed a matrix model for FQH states at filling factor\nu_{k_1k_2} going beyond the Laughlin theory. To illustrate our idea, we haveconsidered an FQH system of a finite number N=(N_{1}+N_{2}) of electrons withfilling factor \nu_{k_{1}k_{2}} = \nu_{p_{1}p_{2}}=\frac{p_{2}}{p_{1}p_{2}-1};p_{1} is an odd integer and p_{2} is an even integer. The \nu_{p_{1}p_{2}}series corresponds just to the level two of the Haldane hierarchy; it recoversthe Laughlin series \nu_{p_{1}} =\frac{1}{p_{1}} by going to the limit p_{2}large and contains several observable FQH states such as \nu = 2/3, 2/5, >....Comment: to be published in the Proceedings (J. Phys. Soc. Japan) of Localisation 2002 Conference, Tokyo, Japa