Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action

Let F be a field of characteristic zero, and let UT2 be the algebra of 2 x 2 upper triangular matrices over F. In a previous paper by Centrone and Yasumura, the authors give a description of the action of Taft's algebras H-m on UT2 and its H-m-identities. In this paper, we give a complete description of the space of multilinear H-m-identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally prove that the variety of H-m-module algebras generated by UT2 has the Specht property, i.e., every T-Hm-ideal containing the H-m-identities of UT2 is finitely based.