Polyhedral Realizations of Crystal Bases for Quantized Kac-Moody Algebras
Abstract
Let B(∞) be the crystal corresponding to the nilpotent part of a quantized Kac-Moody algebra. We suggest a general way to represent B(∞) as the set of integer solutions of a system of linear inequalities. As an application, we treat in a unified manner all Kac-Moody algebras of rank 2 (sharpening the result by Kashiwara), as well as the algebras of types An and An-1(1).
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