Multiplicities in the mixed trace cocharacter sequence of two 3× 3 matrices
Abstract
We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two 3× 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3× 3 matrices.
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