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

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

2005-07-06

arxiv.org/abs/math/0507114v1

Int.Math.Res.Not.2006:10312,2006

Mathematics

Representation Theory

Scientific paper

10.1155/IMRN/2006/10312

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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