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We define and study an action of the symmetric group on the Yokonuma–Hecke algebra. This leads to the definition of two classes of algebras. The first one is connected with the image of the algebra of the braid group inside the Yokonuma–Hecke algebras, and in turn with an algebra defined by Aicardi and Juyumaya known as the algebra of braids and ties. The second one can be seen as new deformations of complex reflection groups of type    G  (  d  ,  p  ,  n  )   . We provide several presentations for both algebras and a complete study of their representation theories using Clifford theory.

Clifford theory for Yokonuma–Hecke algebras and deformation of complex reflection groups