Abstract
(a) The multiplicities m λ in the cocharacter χ n ( A) of (any P.I. algebra A) are polynomially bounded, (b) A hook containing χ n ( A ⊗ B) is obtained from the hooks containing χ n ( A) and χ n ( B). These results are obtained by applying a theory of hook Young diagrams to P.I. algebras, and they generalize results known for algebras satisfying Capelli identities.
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