Heisenberg realization for Uq(sln) on the flag manifold

We give the Heisenberg realization for the quantum algebra U_q(sl_n), which is written by theq-difference operator on the flag manifold. We construct it from the action of U_q(sl_n) on theq-symmetric algebraA_q(Mat_n) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U_q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(\widehat{s1_n })$$ \end{document} [2].