Cohomology of subregular tilting modules for small quantum groups
Abstract
Let
U
be the quantum group with divided powers in
l−
th root of unity and let
u⊂U
be the Frobenius kernel. V.Ginzburg and S.Kumar proved that the cohomology algebra of
u
with trivial coefficients is isomorphic to the functions algebra of the nilpotent cone of the corresponding Lie algebra. In this note we show that there exists tilting module
T
such that the cohomology of
u
with coefficients in
T
is isomorphic to the functions algebra of the closure of the subregular nilpotent orbit.