$ı$Hall algebras of weighted projective lines and quantum symmetric pairs II: injectivity

Abstract

We show that the morphism $\Omega$ from the $ı$quantum loop algebra ${}^{\text{Dr}}\tilde{\mathbf{U}}(L\mathfrak{g})$ of split type to the $ı$Hall algebra of the weighted projective line is injective if $\mathfrak{g}$ is of finite or affine type. As a byproduct, we use the whole $ı$Hall algebra of the cyclic quiver $C_n$ to realise the $ı$quantum loop algebra of affine ${\mathfrak{gl}}_n$.

29 pages. This is the second part of the lengthy paper arXiv:2110.02575v1 which was split into two papers