Pure spinor

In the domain of mathematics known as representation theory, pure spinors (or simple spinors) are spinors that are annihilated, under the Clifford algebra representation, by a maximal isotropic subspace of a vector space ${\displaystyle V}$ with respect to a scalar product ${\displaystyle Q}$. They were introduced by Élie Cartan in the 1930s and further developed by Claude Chevalley.

They are a key ingredient in the study of spin structures and higher dimensional generalizations of twistor theory, introduced by Roger Penrose in the 1960s. They have been applied to the study of supersymmetric Yang-Mills theory in 10D, superstrings, generalized complex structures and parametrizing solutions of integrable hierarchies.