CLASSIFICATION OF ALL PARABOLIC SUBGROUP-SCHEMES OF A REDUCTIVE LINEAR ALGEBRAIC GROUP OVER AN ALGEBRAICALLY CLOSED FIELD

Let G be a reductive linear algebraic group over an algebraically clos ed field K. The classification of all parabolic subgroups of G has bee n known for many years. In that context subgroups of G have been under stood as varieties, i.e. as reduced schemes. Also several nontrivial n onreduced subgroup schemes of G are known, but until now nobody knew h ow many there are and what there structure is. Here I give a classific ation of all parabolic subgroup schemes of G in char(K) > 3.