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We find explicitly the multiplicities in the (mixed) trace cochar- acter 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 con- sequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3× 3 matrices.

MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES