Polynomial invariants of a link with local symmetry

Let D be a link diagram and T a 4-tangle. By replacing each crossing of D by T  , we get a new diagram D⊗TD⊗T, called a link diagram with local symmetry or tensor product of D and T  . In this paper, we will study polynomial invariants of the link diagram D⊗TD⊗T with local symmetry in terms of D and T  , and as an application, we will study the adequacy of D⊗TD⊗T.