Rational representations of general linear groups in algebraic geometry

Nai-Heng Sheu, October 27, 2023

Over a characteristic-zero field, polynomial representations of $\operatorname{GL}(E)$ are constructed from Schur functors $\mathbf S_\lambda(E)$ indexed by partitions $\lambda$ with at most $\dim E$ parts. The Borel–Weil theorem realizes the corresponding irreducible representation, up to the standard dual convention, as global sections of a line bundle on a flag variety. I will explain how these two constructions are related.