The preprojective K-theoretic Hall algebra conjecture for quantum affine algebras

Let $Q$ be a quiver of symmetric Kac–Moody type. Let $\mathrm{KHA}^{\mathbb{C}^*}_{\Pi_Q}$ denote the preprojective K-theoretic Hall algebra of the preprojective algebra $\Pi_Q$, formed from the $\mathbb{C}^*$-equivariant K-theory of its moduli stack of representations. Let $\boldsymbol{\mathrm{U}}^+_{q}(\widehat{\mathfrak{g}_{Q}})^{\text{OS}}$ be the positive part of the Okounkov–Smirnov quantum affine algebra associated with $Q$. The preprojective K-theoretic Hall algebra conjecture. There are isomorphisms of algebras

$$\mathrm{KHA}^{\mathbb{C}^*}_{\Pi_Q} \cong \boldsymbol{\mathrm{U}}^+_{q}(\widehat{\mathfrak{g}_{Q}})^{\text{OS}}.$$

This conjecture is the K-theoretic analogue of the realization of the positive part of the Maulik–Okounkov Yangian by the preprojective cohomological Hall algebra, a result known for quivers of symmetric Kac–Moody type. The K-theoretic realization is presented here as conjectural.