Affine $\mathrm{i}$quantum groups and Steinberg varieties of type C, II

Abstract

A geometric realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(\tau)}$ was given by Wang and the second author, in terms of equivariant K-groups of Steinberg varieties of type C. As a completion of that work, this paper focuses on the previously untreated case. We provide a similar construction of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n}^{(\tau)}$, using the same equivariant K-groups of Steinberg varieties of type C. In the appendix, we employ Steinberg varieties of type D to give a new realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(\tau)}$, thereby avoiding the localization method adopted in the previous work.