Representation stability and finite linear groups
Andy Putman (Rice University)
Wednesday 8th October, 2014 16:00-17:00 Maths 516
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include a proof of Schwartz's Artinian conjecture in the generic representation theory of finite fields and representation-theoretic versions of homological stability for congruence subgroups of the general linear group, the automorphism group of a free group, the symplectic group, and the mapping class group. This is joint with work with Steven Sam.