Algebraic representations and vector bundles

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:

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

2. 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.

3. 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)?

For what concerns 2), you can construct a $$\operatorname{Gl}_n$$-torsor over $$G/B$$ given a representation $$B \to \operatorname{Gl}_n$$ as you suggested. The reasoning should be the following: from the homomorphism $$B \to \operatorname{Gl}_n$$ you get an action of $$B$$ over $$V$$ a complex vector space of dimension $$n$$. You then consider the product variety $$G \times V$$ with the $$B$$ (right) action $$b \cdot(g,x)=(gb,b^{-1}x) .$$
You can check that this action is free and there is a quotient variety $$G \times V/B$$ usually denoted $$G \times_B V$$. The projection onto the first factor $$p:G \times V \to G$$ pasisng to the quotient induces a well defined map $$p: G\times_B V \to G/B$$ which can be checked to be a vector bundle. You can see that the fiber of $$p$$ is actually isomorphic to $$V$$ and so the vector bundle has dimension $$n$$.
Notice that given a $$B$$-invariant subspace $$W$$ you get an embedding of vector bundles $$G \times_B W \subseteq G \times_B V$$ such that the following isomorphism of vector bundles holds $$G \times_B V/W \cong (G \times_B V)/ (G \times_B W) .$$
You then need to find a filtration of $$B$$ representations of $$\mathfrak{u}^{\vee}$$ such that the associated graded piece is isomorphic to the $$1$$-dimensional space $$\mathfrak{u}_{\alpha}$$ for $$\alpha$$ negative roots. This should come from reprentation theory of reductive Lie algebras and reductive groups.