Geodesic
Generalized Dolbeault Sequences in Parabolic Geometry
Journal of Lie theory, Tome 18 (2008) no. 4, pp. 757-773

Voir la notice de l'article provenant de la source Heldermann Verlag

\def\R{{\Bbb R}} We show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. The first operator in this sequence is closely related to the Dirac operator in $k$ Clifford variables, $D=(D_1,\ldots, D_k)$, where $D_i = \sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\SS)\to C^\infty((\R^n)^k, \SS)$. We describe the structure of these sequences in case the dimension $n$ is odd. It follows from the construction that all these operators are invariant with respect to the action of the group $G$. These results are obtained by constructing homomorphisms of generalized Verma modules, which are purely algebraic objects.
Classification : 58J10, 34L40
Mots-clés : Dirac operator, parabolic geometry, BGG, generalized Verma module 
@article{JLT_2008_18_4_JLT_2008_18_4_a1,
     author = {P. Franek },
     title = {Generalized {Dolbeault} {Sequences} in {Parabolic} {Geometry}},
     journal = {Journal of Lie theory},
     pages = {757--773},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_4_JLT_2008_18_4_a1/}
}
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P. Franek . Generalized Dolbeault Sequences in Parabolic Geometry. Journal of Lie theory, Tome 18 (2008) no. 4, pp. 757-773. http://geodesic.mathdoc.fr/item/JLT_2008_18_4_JLT_2008_18_4_a1/