A lower bound for composition multiplicities for the Springer resolution

摘要

Let p : e N. N be the Springer resolution of thenilpotentconefor a semisimpleconnectedalgebraicgroup G over C and k be anarbitrary eld. Whathappensto p * k f N dim e N if thedecompositiontheoremfails forit? Weshowthatinthiscase, someadditional(withrespecttothecase char k= 0) compositionfactorsofthisdirectimageinthe(abelian) categoryof perversesheavesmayemerge. Thesefactorsemergefromthe ZG(x)/ZG(x) 0 compositionfactorsoftheradicalsofcertainintersection formsandfromthat of thetopcohomologiesofSpringer bres(inthenon - sem isimplecase).