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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Trace rings of generic matrices are Cohen-Macaulay


Author: Michel Van den Bergh
Journal: J. Amer. Math. Soc. 2 (1989), 775-799
MSC: Primary 14L30; Secondary 14M05
MathSciNet review: 1001850
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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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DOI: http://dx.doi.org/10.1090/S0894-0347-1989-1001850-7
PII: S 0894-0347(1989)1001850-7
Article copyright: © Copyright 1989 American Mathematical Society