Abstract:
In this talk I will introduce a generalization of the notion of pure spinor with the aim of characterizing Berger's special Riemannnian holonomy groups in a standard way. Recall that complex structures are characterized by pure spinors and Kaehler structures are characterized by (projectively) parallel pure spinors. Thus, we will consider twisted spin groups $Spin(n)\times_{\mathbb{Z}_2} Spin(r)$, their representations, and twisted spinors which induce even Clifford algebra representations on $\mathbb{R}^n$. After defining twisted spin structures, this algebraic set up enables us to characterize special Riemannian holonomies spinorially.