I have some difficulty in understanding the concepts: line bundles, line bundles on a homogeneous space, and sections of line bundles. These concepts are on page 140 (the first paragraph of section 9.3) of the book Young Tableaux by Fulton.
I know that $R \times S^{1}$, where $S^{1}$ is the unit circle and $R$ is the real line, is a line bundle. Möbius strip is also a line bundle. Are there other specific examples of line bundles?
How to understand the sentence in the first paragraph of section 9.3 (page 140) in the book of Fulton clearly: There is a general procedure for producing representations as sections of a line bundle on a homogeneous space?
I also have a question in the first paragraph of the book Young Tableaux on page 131. It is said that if $F$ is a subspace of $E$ of co-dimension $d$, then the kernel of the map from $\wedge^{d}(E)$ to $\wedge^{d}(E/F)$ is a hyperplane in $\wedge^{d}(E)$; assigning this hyperplane to $F$ gives a mapping $Gr^{d}E \to P^{*}(\wedge^{d}E)$. What are the maps $\wedge^{d}(E) \to \wedge^{d}(E/F)$ and $Gr^{d}E \to P^{*}(\wedge^{d}E)$ explicitly?
Thank you very much.