The Principal Representations of Reductive Algebraic Groups with Frobenius Maps

Abstract

We introduce the principal representation category $\mathcal{O}(\mathbf{G})$ of reductive algebraic groups with Frobenius maps and put forward a conjecture that this category is a highest weight category. When $\mathbb{k}$ is complex field $\mathbb{C}$, we provide some evidences of this conjecture. We also study certain kind of bound quiver algebras whose representations are related to the principal representation category $\mathcal{O}(\mathbf{G})$ .

14 pages