Abstract
We compute the exact asymptotics of the codimension sequence for the central polynomials of k × k matrices and show that it is asymptotic to \(\frac{1}{k^2}\) times the ordinary cocharacter. For the other verbally prime algebras we show that these sequences are bounded above and below by constants times the ordinary codimensions.
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Berele, A., Regev, A. Growth of central polynomials of verbally prime algebras. Isr. J. Math. 228, 201–210 (2018). https://doi.org/10.1007/s11856-018-1759-0
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DOI: https://doi.org/10.1007/s11856-018-1759-0