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Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0

Georgia Benkart·Igor Frenkel·Seok-Jin Kang·Hyeonmi Lee
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Abstract

We present a uniform construction of level 1 perfect crystals $\mathcal B$ for all affine Lie algebras. We also introduce the notion of a crystal algebra and give an explicit description of its multiplication. This allows us to determine the energy function on $\mathcal B \otimes \mathcal B$ completely and thereby give a path realization of the basic representations at $q=0$ in the homogeneous picture.

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Georgia Benkart, Igor Frenkel, Seok-Jin Kang, Hyeonmi Lee. 2005-07-06. Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0. https://doi.org/10.1155/imrn/2006/10312

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