This might seem like a silly question considering my relatively elementary knowledge of representation theory.

The question is regarding Eugen Hellman 's paper titled "On the derived category of the Iwahori-Hecke algebra". Specifically on the paragraph above Lemma 2.18. First, let $G$ be a reductive group over a field $C$ of characteristic zero, $B$ a Borel subgroup and $U$ the unipotent radical of $B$. The paper states:

... recall that an algebraic representation of $B$ defines a $G$-equivariant vector bundles on $G/B$. We write $\mathcal{U}^\vee$ for the $G$-equivaraiant vector bundles on $G/B$ defined by the canonical $B$-representation on $\mathfrak{u}^\vee$. Here $\mathfrak{u}$ denotes the Lie algebra of $U$ (considered as a $C$-vector space), and $\mathfrak{u}^\vee$ denotes it's dual. In particular $\mathcal{U}^\vee$ admits a filtration who graded pieces are line bundles $\mathcal{L}_\alpha$ on $G/B$ associated to negative roots (with respect to $B$) roots $\alpha$ of $G$.

My questions are the following:

Firstly, I believe by an algebraic representation, it just means a homomorphism of group schemes $B\rightarrow \operatorname{GL}_n$. Is that correct?

How does such a representation define a vector bundle on $G/B$ ? I am guessing it has something to do with constructing a $\operatorname{GL}_n$-torsor using the representation, but I am not sure how.

Why does $\mathcal{U}^\vee$ admit a filtration into line bundles? (this question might seem silly considering I don't understand how $\mathcal{U}^\vee$ is constructed in the first place)?

Thanks in advance.