I am currently working on an index theory senior project which involves Dirac operators, spin modules and holomorphic induction on the representation ring Lie groups. My primary reference is Sternberg's Lie algebra notes and *Spin Geometry*by Lawson and Michaelson. However I am reading these material very slowly and so far some of the material is still over my head(for example, I do not know how the holomorphic induction works explicitly since I even could not find its definition anywhere), so I am inquiring if there is any elementary article/notes/paper, etc on this topic. All I know is it is essential to under the index theorem at this stage. I am inquiring on here because somehow I lost contact with my advisor.