Abstract
Together, Sections 2 and 5 of this paper form a self contained treatment of the theory of crystals and the path model. It is my hope that this will be useful to the many people who, over the years, have told me that they wished they understood crystals but have found the existing literature too daunting. One goal of the presentation here is to clarify the relationship between the general path model and the crystal operators of Lascoux and Schutzenberger used in the type A case [LS]. More specifically, Section 2 is a basic pictorial exposition of Weyl groups and affine Weyl groups and Section 5 is an exposition of the theory of (a) symmetric functions, (b) crystals and (c) the path model which is designed for readers whose only background is the material in Section 2. These two sections can be read independently of Sections 3 and 4.
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