Braid group action and quasi-split affine iquantum groups III

Abstract

This is the last of three papers on Drinfeld presentations of quasi-split affine iquantum groups ${\tilde{\mathbf{U}}}^{ı}$, settling the remaining type ${\mathrm{AIII}}_{2r}^{(\ddot{I}„)}$. This type distinguishes itself among all quasi-split affine types in having 3 relative root lengths. Various basic real and imaginary $v$-root vectors for ${\tilde{\mathbf{U}}}^{ı}$ are constructed, giving rise to affine rank one subalgebras of ${\tilde{\mathbf{U}}}^{ı}$ associated with simple roots in the finite relative root system. We establish the relations among these $v$-root vectors and show that they provide a Drinfeld presentation of ${\tilde{\mathbf{U}}}^{ı}$.

33 pages