Convexity properties of the canonical S-graphs

2017/01/19 by Joseph, Anthony
#17B35 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1701.05319

Abstract

Let n be a positive integer and c an n-tuple of natural numbers. A convex set in Euclidean n-space given by a family of linear relations in the elements of c and depending on their natural order is defined. The extremal elements of this convex set are shown to be the S-set obtained from the S-graph defined by c constructed in studying the Kashiwara crystal B associated to a Verma module for a Kac-Moody algebra. The result has applications to the precise description of B.

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