Ordinary and graded cocharacter of the Jordan algebra of 2×2 upper triangular matrices

Let F be a field of characteristic zero and UJ2(F) be the Jordan algebra of 2×2 upper triangular matrices over F. In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of Sn. For every Z2-grading of UJ2(F) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.