On the Representation Theory of an Algebra of Braids and Ties

Steen Ryom-Hansen

Published 2008-01-23, updated 2010-04-19Version 4

We consider the algebra ${\cal E}_n(u)$ introduced by F. Aicardi and J. Juyumaya as an abstraction of the Yokonuma-Hecke algebra. We construct a tensor space representation for ${\cal E}_n(u)$ and show that this is faithful. We use it to give a basis for ${\cal E}_n(u)$ and to classify its irreducible representations.