Remarks on the wonderful compactification of semisimple algebraic groups

摘要

We prove that if G is a semisimple algebraic group of adjoin type over the field of complex numbers, H is the subgroup of all fixed numbers, H is the subgroup of all fixed points of an involution σ of G that is induced by an involution σ of the simply connected covering G of G, then the wonderful compactification G/H of the homogeneous space G/H is isomorphic to the G.I.T quotient G~ss(LL)//H of the wonderful compactification G of G for a suitable choice of a line bundle L on G. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of a joint type.