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Questions and conjectures about the modular representation theory of the general linear group GLn(F2) and the Poincar\'e series of unstable modules
This note is devoted to some questions about the representation theory over
the finite field of the general linear groups
and Poincar\'e series of unstable modules. The first draft
was describing two conjectures. They were presented during talks made at VIASM
in summer 2013. Since then one conjecture has been disproved, the other one has
been proved. These results naturally lead to new questions which are going to
be 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 second
one depends on a major topological result: the Segal conjecture. This
discussion could be extended to an odd prime, but we will not do it here, just
a small number of remarks will be made