On the intertwining differential operators between vector bundles over the real projective space of dimension two
Abstract
The main objective of this paper is twofold. One is to classify and construct SL ( 3 , ℝ ) -intertwining differential operators between vector bundles over the real projective space ℝℙ 2 . It turns out that two kinds of operators appear. We call them Cartan operators and PRV operators. The second objective is then to study the representations realized on the kernel of those operators both in the smooth and holomorphic setting. A key machinery is the BGG resolution. In particular, by exploiting some results of Davidson–Enright–Stanke and Enright–Joseph, the irreducible unitary highest weight modules of SU ( 1 , 2 ) at the (first) reduction points are classified by the image of Cartan operators and kernel of PRV operators.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Publication details
- Journal / source
- Journal of Lie Theory
- Volume
- 36
- Issue
- 1
- Pages
- 93–132
- Publication date
- 17 June 2026
- Language
- EN