Trace rings of generic matrices are Cohen-Macaulay

Van den Bergh, Michel

doi:10.1090/S0894-0347-1989-1001850-7

Trace rings of generic matrices are Cohen-Macaulay
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by Michel Van den Bergh

J. Amer. Math. Soc. 2 (1989), 775-799

DOI: https://doi.org/10.1090/S0894-0347-1989-1001850-7

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Abstract:

In this paper, we prove that trace rings of generic matrics are Cohen-Macaulay (Theorem 7.3.6). This is done by relating this problem to a conjecture of Stanley about modules of invariants under a reductive group. We prove a slightly weakened version (Conjecture 3.4’) of this conjecture in special cases (Theorem 6.1.8). In particular, we obtain that Conjecture 3.4’ is true for $S{L_2}$ (Remark 6.1.10).

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Cohen-Macaulayness of modules of invariants for