Victor Reiner
Note on a theorem of Eng

ABSTRACT: We reprove a recent theorem of O. Eng that gives an instance of 
Stembridge's "q=-1 phenomenon" occurring in finite Coxeter groups. Eng's 
proof relied on the classification of irreducible finite Coxeter groups, 
whereas our proof is uniform for Weyl groups. We apply a fact from Hodge 
theory to the cohomology of the homogeneous spaces G/P, where G is a 
semisimple algebraic group and P a parabolic subgroup.