Image of the braid groups inside the finite Iwahori-Hecke algebras
  We determine the image of the braid groups inside the Iwahori-Hecke algebras of type A, when defined over a finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. 
Olivier Brunat, Kay Magaard, Ivan Marin
math.GR math.GT math.RT