Elliptic complex on the Grassmannian of oriented 2-planes

Abstract

The Grassmannian of oriented 2-planes in R^{n+2} where nGREATER-THAN OR EQUAL TO3 carries a homogeneous parabolic conformally symplectic structure of Grassmannian type. The main result of this article is that on the Grassmannian lives an elliptic complex of invariant differential operators of length 3 which starts with the 2-Dirac operator and that the index of the complex is zero.

Keywords

• elliptic complex of differential operators
• Grassmannian manifold
• parabolic contact structure
• symmetry reduction