2011/01/17 by Maakestad, Helge Øystein
#17B20 #17B35 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1101.3134
In this paper we study the scalar generalized Verma module M associated to a character of a parabolic subgroup of SL(E). Here E is a finite dimensional vector space over an algebraically closed field K of characteristic zero. The Verma module M has a canonical simple quotient L with a canonical filtration F. In the case when the quotient L is finite dimensional we use left annihilator ideals in U(\mathfraksl(E)) and geometric results on jet bundles to generalize to an algebraically closed field of characteristic zero a classical formula of W. Smoke on the structure of the jet bundle of a line bundle on an arbitrary quotient SL(E)/P where P is a parabolic subgroup of SL(E). This formula was originally proved by Smoke in 1967 using analytic techniques.