Gradings on the algebra of upper triangular matrices and their graded identities

Let K be an infinite field and denote UTn(K) the algebra of n x n upper triangular matrices over K. We describe all elementary gradings on this algebra. Further we produce linear bases of the respective relatively free graded algebras, and prove that one can distinguish the elementary gradings by their graded identities. We describe bases of the graded polynomial identities in several "typical" cases. Although we consider elementary gradings by the cyclic group of order two the same methods serve for elementary gradings by any finite group.An extended version of this report will be published elsewhere.