Non-Cohen-Macaulay invariant rings of infinite groups
Let \(K\) be an algebraically closed field of positive characteristic. In this paper there are given some explicit examples of invariant rings that are not Cohen-Macaulay for all classical groups SL\(_{n}(K)\), GL\(_{n}(K)\), Sp\(_{2n}(K) \), SO\(_{n}(K)\) and O\(_{n}(K)\). It is also proved that every non-trivial unipotent group over \(K\) has representations such that the invariant ring is not Cohen-Macaulay (see Section 4). All results of the paper are new and carefully proved. The manner of presenting is clear, with many examples, and so the paper contributes to the development of this important research domain.
scientific article; zbMATH DE number 5115360