Image of the braid groups inside the finite Temperley-Lieb algebras

2012/03/23 by Olivier Brunat, Brunat, Olivier, Ivan Marin +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.GT #math.RT

paper · pdf · doi:10.48550/arxiv.1203.5210

minor revision

arxiv created 2014/01/22 · arxiv updated 2014/01/23

Abstract

We determine the image of the braid groups inside the Temperley-Lieb algebras, defined over finite field, in the semisimple case, and for suitably large (but controlable) order of the defining (quantum) parameter. We also prove that, under natural conditions on this parameter, the representations of the Hecke algebras over a finite field are unitary for the action of the braid groups.

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