Pure Spinors on Lie groups

Details Pure Spinors on Lie groups Pure Spinors on Lie groups

2007-09-10

arxiv.org/abs/0709.1452v2

Ast\'erisque No. 327 (2009), 131-199 (2010)

Mathematics

Differential Geometry

63 pages. v2: minor changes, typos fixed. To appear in Asterisque

Scientific paper

For any manifold M, the direct sum TM \oplus T*M carries a natural inner product given by the pairing of vectors and covectors. Differential forms on M may be viewed as spinors for the corresponding Clifford bundle, and in particular there is a notion of \emph{pure spinor}. In this paper, we study pure spinors and Dirac structures in the case when M=G is a Lie group with a bi-invariant pseudo-Riemannian metric, e.g. G semi-simple. The applications of our theory include the construction of distinguished volume forms on conjugacy classes in G, and a new approach to the theory of quasi-Hamiltonian G-spaces.

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