Quantum loop groups and K$K$‐theoretic stable envelopes

We develop the connection between the preprojective ‐theoretic Hall algebra [Schiffmann and Vasserot (Duke Math. J. 162 (2013), no. 2, 279–366), Yang and Zhao (Proc. London Math. Soc. (3) 116 (2018), no. 5, 1029–1074)] of a quiver and the quantum loop group associated to via stable envelopes of Nakajima quiver varieties [Okounkov and Smirnov (Invent. Math. 229 (2022), 1203–1299)].