Title: Rings of Generalized and Stable Invariants
of Pseudoreflections and Pseudoreflection Groups
Authors: Frank Neumann, Mara D. Neusel and Larry Smith
Abstract: Let \rho: G --> GL(n, F) be a representation of a finite
group G over the field F and F[V] the space of polynomial functions
on V=F^n. We associate to G an ideal J_\infty(G) of F[V] called the
ideal of stable invariants of \rho. If S is a set of pseudoreflections
we associate to S the ideal I(S) of F[V] called the ideal of generalized
invariants of S in the sense of Kac and Peterson.
When G is a pseudoreflection group we investigate I(S) for various choices
of S and the relation between J_\infty(G) and I(S).
To a representation \rho, respectively to a set S of pseudoreflections,
we also associate the rings gr_J_\infty(G) respectively gr_I(S) of
stable and generalized invariants. We show that gr_I(S) is always a
polynomial algebra over F and whenever \rho(G) is generated by semisimple
pseudoreflections S that gr_J_\infty(G)=gr_I(S).
This is the version which is published in J. of Algebra 182 (1996), 85-122.