Depth and detection in modular invariant theory

Elmer, Jonathan ORCID: (2009) Depth and detection in modular invariant theory. Journal of Algebra, 322 (5) . pp. 1653-1666. ISSN 0021-8693 (doi:10.1016/j.jalgebra.2009.04.036)

PDF - First submitted uncorrected version (with author's formatting)
Download (551kB) | Preview


Let G be a finite group acting linearly on a vector space V over a field of characteristic p dividing the group order, and let R denote S(V∗). We study the R^G modules H^i(G, R), for i ≥ 0 with R^G itself as a special case. There are lower bounds for depth of (H^i(G, R)) and for depth(R^G). We show that a certain sufficient condition for their attainment (due to Fleischmann, Kemper and Shank) may be modified to give a condition which is both necessary and sufficient. We apply our main result to classify the representations of the Klein four-group for which depth(R^G) attains its lower bound. We also use our new condition to show that the if G = P × Q, with P a p-group and Q an abelian p'-group, then the depth of R G attains its lower bound if and only if the depth of R^P does so.

Item Type: Article
Additional Information: Available online 12 May 2009
Research Areas: A. > School of Science and Technology > Design Engineering and Mathematics
Item ID: 19270
Useful Links:
Depositing User: Jonathan Elmer
Date Deposited: 14 Apr 2016 10:56
Last Modified: 15 Oct 2019 00:17

Actions (login required)

Edit Item Edit Item

Full text downloads (NB count will be zero if no full text documents are attached to the record)

Downloads per month over the past year