# Twisted pure spinors and Riemannian holonomy

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Rafael Herrera

created by risa on 10 Jul 2015

16 jul 2015
-- 14:30

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

**Abstract.**

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.