The Elliptic Algebra [inline-graphic not available: see fulltext] and the Drinfeld Realization of the Elliptic Quantum Group [inline-graphic not available: see fulltext]

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra [inline-graphic not available: see fulltext], we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group [inline-graphic not available: see fulltext]. For this purpose, we introduce a set of new currents \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$K_j(v) (1\leq j\leq N)$\end{document} in [inline-graphic not available: see fulltext]. As in the N=2 case, we find a structure of [inline-graphic not available: see fulltext] as a certain tensor product of [inline-graphic not available: see fulltext] and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in [inline-graphic not available: see fulltext]. Using the coalgebra structure of [inline-graphic not available: see fulltext] and the above tensor structure, we derive a free field realization of the [inline-graphic not available: see fulltext]-analogue of [inline-graphic not available: see fulltext]-intertwining operators. The resultant operators coincide with those of the vertex operators in the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A_{N-1}^{(1)}$\end{document}-type face model.