Cohomology of Subregular Tilting Modules for Small Quantum Groups

Abstract

Let U be a quantumgroup with divid d powers at root ofunity constructed froma root system R .Let u U b th small quantumgroup. The cohomology of u with trivial coefficients was computed by Ginzburg and Kumar. It turns out to be isomorphic to the functions algebra of the nilpotent cone of a semisimpl algebraic group with root system R. In this not we calculate cohomology of u with coefficients in simplest reducible tilting modul with nontrivial cohomology. It appears to b isomorphic to th functions algebra of th closure of the subregular nilpotent orbit.