English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This note is devoted to some questions about the representation theory overthe finite field $\mathbb{F}_2$ of the general linear groups$\mathbb{GL_n(F_2)}$ and Poincar\'e series of unstable modules. The first draftwas describing two conjectures. They were presented during talks made at VIASMin summer 2013. Since then one conjecture has been disproved, the other one hasbeen proved. These results naturally lead to new questions which are going tobe discussed. In winter 2013, Nguyen Dang Ho Hai proved the second conjecture,he disproved the first one in spring 2014. Up to now, the proof of the secondone depends on a major topological result: the Segal conjecture. Thisdiscussion could be extended to an odd prime, but we will not do it here, justa small number of remarks will be made.

Questions and conjectures about the modular representation theory of the general linear group GLn(F2) and the Poincar\'e series of unstable modules