Finiteness properties of the Steinberg representation
We will show that the Steinberg modules for the general linear groups form a Koszul monoid in
an appropriate symmetric monoidal category. Using this we will find bounds on the
codimension-one cohomology of level-3 congruence subgroups. This Koszulness result can also
be used to show Ash–Putman–Sam homological vanishing theorem for the Steinberg
representations. This is a joint work with Jeremy Miller and Peter Patzt.