A matrix M is invertible under ã if and only if the diagonal entries are nonzero. The set of invertible matrices under ã is a solvable Lie group, with the invertible diagonal matrices T serving as a maximal torus, and with unipotent radical U the set of all matrices with ones along the diagonal.As a consequence, Knutson and Zinn Justin were able to classify all the top dimensional irreducible components of E and to give a partial set of equations for the top dimensional components of E. Moreover, they compute the multidegree of these top dimensional components and connect that polynomial to the entries of the Frobenius-Perron eigenvector of a certain Markov process associated to the Brauer loop model...