The (apparent, supposed) mathematics behind the fractional quantum hall effect involves the TQFT invariants coming from representations of quantum groups at roots of unity.

The (apparent, supposed) mathematics behind the fractional quantum hall effect involves the TQFT invariants coming from representations of quantum groups at roots of unity.

Edit: some links for further reading:

• From String Nets to Nonabelions
• A class of P,T-invariant topological phases of interacting electrons
• Topological quantum computation