Automorphism groups of Codes associated to the Grassmannian and its Schubert divisor
Krishna V. Kaipa
We begin with a brief introduction to linear codes from the geometric viewpoint. We are interested in linear codes associated with the Grassmannian, its Schubert cells, and Schubert varieties. In particular their automorphism groups. We discuss Chow's thorem about adjacency preserving bijections of the Grassmannian over arbitrary fields. We extend this result to bijections of the big cell of the Grassmannian. We then go into a more in-depth study of the geometry of the Schubert divisor of the Grassmannian and determine its automorphism group (over arbitrary fields).