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Codimensions and trace codimensions of matrices are asymptotically equal

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Abstract

The codimensionsc n and the trace codimensionst n of thek×k matrices are asymptotically equal: lim n→∞(t n /c n )=1. Sincet n ≅q(n)·k 2n whereq(x) is a known rational function, this asymptotically givesc n . This has applications to the codimensions of Capelli identities.

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Authors and Affiliations

  1. Department of Theoretical Mathematics, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Amitai Regev

  2. Department of Mathematics, Brandeis University, 02159, Waltham, MA, USA

    Amitai Regev

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  1. Amitai Regev
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Regev, A. Codimensions and trace codimensions of matrices are asymptotically equal. Israel J. Math. 47, 246–250 (1984). https://doi.org/10.1007/BF02760520

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  • DOI: https://doi.org/10.1007/BF02760520

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