Differential operator realization of braid group action on ıquantum groups

Abstract

We construct a unique braid group action on deformed q-Weyl algebra Aq(S). Under this action, we give a realization of the braid group action on quasi-split ıquantum groups U(S)ı of type AIII. Furthermore, we directly construct a unique braid group action on polynomial ring P which is compatible with the braid group action on Aq(S) and U(S)ı.