Invarianten zusammenh\"angender Gruppen und die Cohen-Macaulay Eigenschaft

TL;DR

This paper constructs specific representations of the groups SL_n and GL_n where the invariant rings fail to have the Cohen-Macaulay property, highlighting limitations in invariant theory.

Contribution

It provides explicit examples of representations with non-Cohen-Macaulay invariant rings for SL_n and GL_n, advancing understanding of invariant ring properties.

Findings

Invariant rings for certain representations are not Cohen-Macaulay.

Explicit constructions for SL_n and GL_n representations.

Highlights limitations of Cohen-Macaulay property in invariant theory.

Abstract

For G=SL_n or GL_n we construct representations V such that the invariant ring K[V]^G is not Cohen-Macaulay.