Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0
Abstract
We present a uniform construction of level 1 perfect crystals 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 B B completely and thereby give a path realization of the basic representations at q=0 in the homogeneous picture.
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