An algebraic groups perspective on Erd\H{o}s-Ko-Rado

Abstract

We give a proof of the Erd\H{o}s-Ko-Rado Theorem using the Borel Fixed Point Theorem from algebraic group theory. This perspective gives a strong analogy between the Erd\H{o}s-Ko-Rado Theorem and (generalizations of) the Gerstenhaber Theorem on spaces of nilpotent matrices.