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 $u\subset U$ 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.