Quantum roots for Kac-Moody root systems and finiteness properties of the Kac-Moody affine Bruhat order

Auguste Hebert, Paul Philippe

Let $G$ be a split Kac-Moody group over a local field. In their study of the Iwahori-Hecke algebra of $G$, A.Braverman, D. Kazhdan and M. Patnaik defined a partial order - called t…