Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Twisted pure spinors and Riemannian holonomy

Rafael Herrera

created by risa on 10 Jul 2015

16 jul 2015 -- 14:30

Aula di Consiglio, Dip. Matematica, Università "La Sapienza", Roma


In this talk I will introduce a generalizaton 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 setup enables us to characterize special Riemannian holonomies spinorially.

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