Let $\mathbb{K} \subset \mathbb{T}$ be two tori acting on a topological space $X$ (with all the properties you want). We use the notations $$X_{\mathbb{T}} := (X \times E \mathbb{T}) / \mathbb{T}, \quad X_{\mathbb{K}} := (X \times E \mathbb{K}) / \mathbb{K}$$ for the homotopy quotients.

The space $E \mathbb{T}$ can be considered as $E \mathbb{K}$ if provided with the $\mathbb{K}$-action, and therefore there exists a fibration $$X_{\mathbb{K}} \overset{\mathbb{T} / \mathbb{K}}{\longrightarrow} X_{\mathbb{T}}.$$

The Serre spectral sequence associated with this fibration has $E_2$-term $$E_2^{pq} = H^p(X_{\mathbb{T}}) \otimes H^q(\mathbb{T} / \mathbb{K}),$$ and converges to $H^{p+q}(X_{\mathbb{K}})$.

I am trying to understand what the transgression map is here, and more precisely what are the images of the generators of $H^*(\mathbb{T} / \mathbb{K})$ in $H^2(B \mathbb{T})$.

Moreover, I read somewhere that this $E_2$-term is the Koszul complex of these images (of degree $2$) in the algebra $H^p(X_{\mathbb{T}})$. What does this mean ?

Thanks a lot