Bosonic representations of Yangian Double $\cD Y_{\hbar}(\gtg)$ with $\gtg=\gtgl_N,\gtsl_N$

Kenji Iohara

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Bosonic representations of Yangian Double $\cD Y_{\hbar}(\gtg)$ with $\gtg=\gtgl_N,\gtsl_N$

Kenji Iohara

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Abstract

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.

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BibTeX RIS

Kenji Iohara. 1996-04-01. Bosonic representations of Yangian Double $\cD Y_{\hbar}(\gtg)$ with $\gtg=\gtgl_N,\gtsl_N$. https://arxiv.org/abs/q-alg/9603033

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