Let $\fg$ be a finite dimensional simple Lie algebra over the complex numbers. Consider the exterior algebra $R := \wed (\fg\oplus\fg )$ on two copies of $\fg$. Then, the algebra $R$ is bigraded with the two copies of $\fg$ sitting in bidegrees (1,0) and (0,1) respectively. To distinguish, we denote them by $\fg_1$ and $\fg_2$ respectively. The diagonal adjoint action of $\fg$ gives rise to a $\fg$-algebra structure on $R$ compatible with the bigrading. We isolate three `standard' copies of the adjoint representation $\fg$ in the total degree $2$ component $R^2$. The $\fg$-module map $ \part : \fg \to \wed^2(\fg ), \,x\mapsto \part x = \sum_i [x,e_i]\wed f_i, $ considered as a map to $\wed^2(\fg_1)$ will be denoted by $c_1$, and similarly, $c_2: \fg \to \wed^2(\fg_2),$ and $c_3 : \fg \to \fg_1\otimes\fg_2, \,x\mapsto \sum_i\, [x,e_i]\otimes f_i,$ where $\{ e_i\}_{i\leq i\leq N}$ is any basis of $\fg$ and $\{ f_i\}_{1\leq i\leq N}$ is the dual basis of $\fg$ with respect to the Killing form. We denote by $C_i$ the image of $c_i$. Let $J$ be the (bigraded) ideal of $R$ generated by the three copies $C_1, C_2, C_3$ of $\fg$ (in $R^2$) and define the bigraded $\fg$-algebra $A := R/J.$ The Killing form gives rise to a $\fg$-invariant $S\in A^{1,1}$. Motivated by supersymmetric gauge theory, Cachazo-Douglas-Seiberg-Witten made the following conjecture. \noindent {\bf Conjecture} (i) The subalgebra $A^{\fg}$ of $\fg$-invariants in $A$ is generated, as an algebra, by the element $S$. (ii) $S^h =0$. (iii) $S^{h-1}\neq 0$. The aim of this talk is to give a uniform proof of the above conjecture part (i). In addition, we give a conjecture, the validity of which would imply part (ii) of the above conjecture. The main ingredients in the proof are: Garland's result on the Lie algebra cohomology of $\hat{\fu} := \fg\otimes t\bc [t]$; Kostant's result on the `diagonal' cohomolgy of $\hat{\fu}$ and its connection with abelian ideals in a Borel subalgebra of $\fg$; and a certain deformation of the singular cohomology of the infinite Grassmannian introduced by Belkale-Kumar.