Let F be a field of characteristic zero and UJ_2(F) be the Jordan algebra of 2x2 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 S_n. For every Z_2-grading of UJ_2(F) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
Cirrito, A., Martino, F. (2014). Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices. LINEAR ALGEBRA AND ITS APPLICATIONS, 451, 246-259 [10.1016/j.laa.2014.03.011].
Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices
CIRRITO, Alessio
;MARTINO, Fabrizio
2014-01-01
Abstract
Let F be a field of characteristic zero and UJ_2(F) be the Jordan algebra of 2x2 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 S_n. For every Z_2-grading of UJ_2(F) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
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