image-graded cocharacters for superalgebras of triangular matrices

Let image be a field of characteristic zero, let A, B be image-algebras with polynomial identity and let M be a free (A,B)-bimodule. The algebra image can be endowed with a natural image-grading. In this paper, we compute the graded cocharacter sequence, the graded codimension sequence and the superexponent of R. As a consequence of these results, we also study the above PI-invariants in the setting of upper triangular matrices. In particular, we completely classify the algebra of 3×3 upper triangular matrices endowed with all possible image-gradings.