Degree bounds--an invitation to postmodern invariant theory
Mara D. Neusel
Mara.D.Neusel@ttu.edu
Abstract:
This is a survey article on degree bounds in invariant theory of finite
groups. A finite subgroup $G$ of the general linear group $\GL(n\, \F)$
over some field $\F$ acts via matrix multiplication on the vector space
$V=\F^n$. This induces an action of $G$ on the polynomials $\F[x_1\commadots
x_n]$ in $n$ variables. The polynomials $\F[x_1\commadots x_n]^G\subseteq
\F[x_1\commadots x_n]$ invariant under this action form a subring.
This ring is our center of study. In particular we will discuss
how to calculate this ring. In this context degree bounds are 
central, and we want to present the known results.
We also sketch the techniques that are used
to obtain good bounds and describe open questions.