Generalized Verma module homomorphisms in singular character. (English) Zbl 1164.22310

Franek, Peter

Arch. Math., Brno 42, No. 5, 229-240 (2006).

Summary: 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 the 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.

MSC:

22E47	Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
17B10	Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
58J60	Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)

Keywords:

parabolic structure; invariant differential operator; Dirac operator; Verma module