Generalized Verma module homomorphisms in singular character

Peter Franek

Charles University, Faculty of Mathematics and Physics, Sokolovska 83, 186 75 Praha 8, Czech Republic


In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the $k$-th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.