Homomorphisms between Verma Modules in Characteristic P
نویسنده
چکیده
Let g be a complex semisimple Lie algebra, with a Bore1 subalgebra b c g and Cartan subalgebra h c b. In classifying the finite dimensional representations of g, Cartan showed that any simple finite dimensional g-module has a generating element u, annihilated by n = [b, b], on which h acts by a linear form I E h*. Such an element is called a primitive vector (for the module). Harish-Chandra [9] considered g-modules, not necessarily finite dimensional, with a primitive vector, in particular the “universal” modules of this kind, called “Verma modules” by Dixmier [7]. These are constructed using the universal enveloping algebra % of g: the Verma module corresponding to I is
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