# Tag Archives: representations

## Highlights in Linear Algebraic Groups 7: Representations II

In the previous post, we saw that if $G\times X\to X$ is an algebraic group acting on a variety $X$ and $F\subseteq k[X]$ is a finite-dimensional subspace then there exists a finite dimensional subspace $E\subseteq k[X]$ with $E\supseteq F$ such that $E$ is invariant under translations. Recall that if […]

## Highlights in Linear Algebraic Groups 6: Representations I

Soon it will be time to explore some aspects of root systems and structure theory for reductive groups. Our goal is to understand everything in the classical setting over an algebraically closed field, and then explore reductive groups over arbitrary base schemes. Before we do this, I will give a few examples for some of […]