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Let $K$ be a field of characteristic zero and $V$ a vector space of dimension$m>1$ with a nondegenerate symmetric bilinear form $f:V\times V \rightarrow K$.The Jordan algebra $B_m=K\oplus V$ of the form $f$ is a superalgebra with thisdecomposition. We prove that the ideal of all the $2$-graded identities of$B_m$ satisfies the Specht property and we compute the $2$-graded cocharactersequence of $B_m$.

Specht property for the $2$-graded identities of $B_m$