
School of Mathematics and Statistics
Gregor Kemper Universität Heidelberg
The CohenMacaulay Property in Invariant Theory
Friday 3rd July, 121pm, Carslaw 273.
A theorem of Hochster and Eagon says that invariant rings of a
finite group G over a field K such that char(K)
does not divide
G are CohenMacaulay, i.e., they are free modules of finite rank
over a polynomial subalgebra. This is a very important structural
property with high relevance for computations.
This talk gives an
introduction into the CohenMacaulay property and then goes on to
explain the following converse to the theorem of Hochster and Eagon:
if for every representation of G over K the invariant ring
is CohenMacaulay, then char(K) does not divide G. More
results come out of this work, such as a classification of all finite groups
G and fields K such that the invariant ring of the regular
representation over K is CohenMacaulay. Furthermore, if G is a
linear pgroup, p = char(K), and the invariant
ring of G is CohenMacaulay, then G is generated by
bireflections.
