BRAID GROUP ACTION AND QUASI-SPLIT AFFINE iQUANTUM GROUPS I

This is the first of our papers on quasi-split affine quantum symmetric pairs (U) over tilde ((g) over cap), (U) over tilde (i), focusing on the real rank one case, i.e., g = sl(3) equipped with a diagram involution. We construct explicitly a relative braid group action of type A(2)((2)) on the affine iquantum group (U) over tilde (i). Real and imaginary root vectors for (U) over tilde (i) are constructed, and a Drinfeld type presentation of (U) over tilde (i) is then established. This provides a new basic ingredient for the Drinfeld type presentation of higher rank quasi-split affine iquantum groups in the sequels.