Computing Optimal Descriptions of Stratifications of Actions of Compact Lie Groups

We provide a constructive approach to the stratification of the representation- and the orbit space of linear actions of compact Lie groups contained in $\GLn \R$ on $\Realn n$ and we show that any $d$-dimensional stratum, respectively, its closure can be described by $d$ sharp, respectively, relaxed polynomial inequalities and that $d$ is also a lower bound for both cases. Strata of the representation space are described as differences of closed sets given by polynomial equations while $d$-dimensional strata of the orbit space are represented by means of polynomial equations and inequalities. All algorithms have been implemented in {\sc SINGULAR V2.0}.     «

We provide a constructive approach to the stratification of the representation- and the orbit space of linear actions of compact Lie groups contained in $\GLn \R$ on $\Realn n$ and we show that any $d$-dimensional stratum, respectively, its closure can be described by $d$ sharp, respectively, relaxed polynomial inequalities and that $d$ is also a lower bound for both cases. Strata of the representation space are described as differences of closed sets given by polynomial equations while $d$-dime...     »