1
vote
1answer
96 views

Definition of differential of Adjoint representation of Lie Group

Let $g$ be an element of Lie Group $G$, and $\gamma(t) : \mathbb{R} \rightarrow G$ be a path in $G$ such that $\gamma(0) = e$, the identity element of $G$. Denote the tangent space at $e$ as $T_eG$, ...
6
votes
3answers
361 views

Lie algebra action from Lie group action: coordinates

Here's the setup: I have $SL(2;\mathbb{C})$ acting on $V = \mathbb{C}[z,w] = \oplus_d V_d$, where $V_d$ is the homogeneous complex polynomials of degree $d$. The action is precomposition: ...
4
votes
2answers
235 views

what are good references for learning about vector bundles and their sheaves of sections?

I am a beginner in representation theory and algebraic geometry, so that references giving clear explanations of things like the tautological line bundle on $\mathbb P^n$, its dual, and the associated ...