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.

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