Twisted Whittaker modules over U-q(gl(n+1))

As is well known, the classical nonsingular Whittaker modules over quantum groups cannot be defined for non A1-type. In this paper, by choosing different generators for the quantum group U-q(gl(n+1)), we introduce and study the twisted Whittaker modules over U-q(gl(n+1)). We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions. This agrees Kostant's results on Whittaker modules for the simple complex Lie algebras sl(n+1) as q approaches 1.