Elliptic complex on the Grassmannian of oriented 2-planes

Abstract

The Grassmannian $V_2({\mathbb{R}}^{n+2})$ of oriented 2-planes in ${\mathbb{R}}^{n+2}$ where $n\ge 3$ carries a homogeneous parabolic contact structure of Grassmannian type. The main result of this article is that on $V_2({\mathbb{R}}^{n+2})$ 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.

revised version, comments are welcome

References in corpus (3)

• Parabolic conformally symplectic structures II; parabolic contactification
• Parabolic conformally symplectic structures III; Invariant differential operators and complexes
• $k$-Dirac Complexes