Steen Ryom-Hansen: The representation theory of the Yokonuma-Hecke algebra and related algebras

This is an account of joint work with J. Espinoza. The Yokonuma-Hecke algebra YH has received much interest lately, particularly from the point of view of knot theory. In this talk we shall study the representation theory of YH and the representation theory of its subalgebra E, the algebra of braids and ties introduced by Aicardi and Juyumaya. It has a basis involving set partitions, but for general parameters its relationship with the partition algebra of V. Jones and P. Martin is still unclear. We construct faithful tensor space modules for both algebras. This allows us to produce a concrete isomorphism between YH and Shoji's modified Ariki-Koike algebra. Finally, we obtain a cellular basis structure on E.