Penrose transform and monogenic sections. (Q2846614)

Let \(M\) be the Grassmannian of isotropic planes in a vector space of dimension \(n+4\) which is endowed with an inner product of signature \((n+2,2)\). This is the homogeneous model for a certain parabolic geometry, which leads to a BGG-sequence (in singular infinitesimal character) starting with the so-called 2-Dirac operator. The article studies the kernel of this operator (restricted to an open cell in \(M\)) using the Penrose transform. This kernel is the space of monogenic sections, which is important in Clifford analysis, thus leading to interesting potential applications of the article.NEWLINENEWLINEA large part of the article is devoted to making the Penrose transform explicit in this case. The main result of the article is a description of the space of monogenic spinors in terms of representation theory.