Spinor structures on flag manifolds of compact simple Lie groups

Abstract

In this paper spinor structures over flag manifolds of compact simple Lie groups are considered and constructed explicitly, using the general method of Dabrowski and Trautman. In this way the existence and uniqueness of these structures is established, in accordance with purely topological results of Freed. Application of the structures for further studies of fermionic excitations in theories with coadjoint orbits as phase spaces, including infinite-dimensional systems such as superfluid helium, is suggested.