Let *T* be an arbitrary compact torus.
The second cohomology group of *BT* (with arbitrary coefficients, call that ring <i>k</i>) generates the full cohomology freely as an algebra. In other words, if you pick a <i>k</i>-basis *x*<sub>1</sub>, *x*<sub>2</sub>,... of *H*<sup>2</sup>(*BT*), then you get an isomorphism of <i>H</i>*(*BT*) with <i>k</i>[<i>x</i><sub>1</sub>, *x*<sub>2</sub>,...].
Now let's specialise to the case *k*=ℤ. In that case, the second cohomology group of *BT* is canonically isomorphic to the group of characters of *T*, i.e., to the group of homomorphisms from *T* → *S*<sup>1</sup>. Given a character χ :*T* → *S*<sup>1</sup>, the corresponding element of *H*<sup>2</sup>(*BT*) is represented by (the first Chern class of) the complex line bundle *ET* ×<sub>T</sub> ℂ<sub>χ</sub>.
Now back to your question. The elements α<sub>1</sub> and α<sub>2</sub> form a basis of *BT*, where *T* now refers to the maximal torus of *G*<sub>2</sub>. So you get an isomorphism <i>H</i>*(*BT*;ℤ) $\xrightarrow{\sim}$ ℤ[α<sub>1</sub>, α<sub>2</sub>]. But
λ<sub>1</sub> and λ<sub>2</sub> also form a basis of *BT*. So you get another isomoprhism <i>H</i>*(*BT*;ℤ) $\xrightarrow{\sim}$ ℤ[λ<sub>1</sub>, λ<sub>2</sub>].