A class of representations of Artin braid hypergroups

Hypergroup is the generalized concept of group introduced first by Marty. Since then, the study of it and its applications has been of great importance. This paper deals with representations of the hypergroup associated to the braid group B-n. First, we define our hypergroup (B-n, *) and our semihyperring (P, circle plus, circle dot) over the set of non-negative integers. Next, we construct non-trivial matrix representations of B-n of degree k, for all k is an element of N. Finally, we find all matrix representations of (B-n, *) with degree less than 3 and classify them according to irreducibility and unitarizability.