The tensor product of <i>m</i> -partition algebras as a centralizer algebra of An1×An2×⋯×Anm

In this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor products [Formula: see text], where [Formula: see text]. In particular, we restrict the action of the direct products of symmetric groups, [Formula: see text], to the action of the direct product of alternating groups, [Formula: see text]. Herein, we determine the basis for the centralizer algebra and exhibit that when the centralizer is isomorphic to the tensor product of m-partition algebras, [Formula: see text].