Pure Spinors on Lie groups

Abstract

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.

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

References in corpus (1)

• The modular class of a twisted Poisson structure

Cited by in corpus (5)

• Poisson Manifolds, Lie Algebroids, Modular Classes: a Survey
• Quasi-Hamiltonian groupoids and multiplicative Manin pairs
• Generalized Kahler geometry
• Courant morphisms and moment maps
• Two Categories of Dirac Manifolds