两个$3\times 3$矩阵的混合迹余特征标序列的重数
Multiplicities in the mixed trace cocharacter sequence of two $3\times 3$ matrices
摘要:
我们发现明确的多重性的(混合)迹余特征序列的两个$3\times 3$矩阵在一个字段的特征为0,并表明,渐近他们表现为多项式的第七次。作为结果,我们还获得了某些不可约字符的重数在$3\times 3$矩阵的多项式身份的余特征标序列。
英文摘要:
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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