On the double-affine Bruhat order: the $\epsilon =1$ conjecture and classification of covers in ADE type

Dinakar Muthiah, Daniel Orr

For any Kac-Moody group $\mathbf{G}$, we prove that the Bruhat order on the semidirect product of the Weyl group and the Tits cone for $\mathbf{G}$ is strictly compatible with a $\…