Bosonic representations of Yangian Double $\cD Y_{\hbar}(\gtg)$ with $\gtg=\gtgl_N,\gtsl_N$
Abstract
Description
On the basis of `$RTT=TTR$' formalism, we introduce the quantum double of the Yangian $Y_{\hbar}(\gtg)$ for $\gtg=\gtgl_N,\gtsl_N$ with a central extension. The Gauss decomposition of T-matrices gives us the so-called Drinfel'd generators. Using these generators, we present some examples of both finite and infinite dimensional representations that are quite natural deformations of the corresponding affine counterpart.
33 pages, AmsLatex file, Submitted to Jour. of Phys. A
33 pages, AmsLatex file, Submitted to Jour. of Phys. A