Previous |  Up |  Next


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.
[1] Cap A., Slovák J.: Parabolic geometries. preprint Zbl 1183.53002
[2] Eastwood M.: Conformally invariant differential operators on Minkowski space and their curved analogues. Comm. Math. Phys. bf 109 2 (1987), 207–228. MR 0880414 | Zbl 0659.53047
[3] Goodman R., Wallach N.: Representations and invariants of the classical groups. Cambgidge University Press, Cambridge, 1998. MR 1606831 | Zbl 0901.22001
[4] Slovák J., Souček V.: 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
[5] Bureš J., Souček V.: Regular spinor valued mappings. Seminarii di Geometria, Bologna 1984, ed. S. Coen, Bologna, 1986, 7–22. MR 0877529
Partner of
EuDML logo