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.
@article{108029,
author = {Peter Franek},
title = {Generalized Verma module homomorphisms in singular character},
journal = {Archivum Mathematicum},
volume = {042},
year = {2006},
pages = {229-240},
zbl = {1164.22310},
mrnumber = {2322409},
language = {en},
url = {http://dml.mathdoc.fr/item/108029}
}
Franek, Peter. Generalized Verma module homomorphisms in singular character. Archivum Mathematicum, Tome 042 (2006) pp. 229-240. http://gdmltest.u-ga.fr/item/108029/
Parabolic geometries, preprint | Zbl 1183.53002
Conformally invariant differential operators on Minkowski space and their curved analogues, Comm. Math. Phys. bf 109 2 (1987), 207–228. (1987) | MR 0880414 | Zbl 0659.53047
Representations and invariants of the classical groups, Cambgidge University Press, Cambridge, 1998. (1998) | MR 1606831 | Zbl 0901.22001
Invariant operators of the first order on manifolds with a given parabolic structure, Seminarires et congres 4, SMF, 2000, 251-276. | MR 1822364 | Zbl 0998.53021
Regular spinor valued mappings, Seminarii di Geometria, Bologna 1984, ed. S. Coen, Bologna, 1986, 7–22. (1984) | MR 0877529