Abstract
Let M1,2(F) be the algebra of 3×3 matrices with orthosymplectic superinvolution ⁎ over a field F of characteristic zero. We study the ⁎-identities of this algebra through the representation theory of the group Hn=(Z2×Z2)∼Sn. We decompose the space of multilinear ⁎-identities of degree n into the sum of irreducibles under the Hn-action in order to study the irreducible characters appearing in this decomposition with non-zero multiplicity. Moreover, by using the representation theory of the general linear group, we determine all the ⁎-polynomial identities of M1,2(F) up to degree 3.
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