Multiplicities in the mixed trace cocharacter sequence of two $3\times 3$ matrices

Mathematics – Rings and Algebras

Scientific paper

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LATEX file, 9 pages

Scientific paper

We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two $3\times 3$ 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 $3\times 3$ matrices.

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