Abstract

The main purpose of this paper is to give a combinatorial realization of Kirillov-Reshetikhin (KR simply) crystals Br,s for type En(1) with a minuscule node r and s≥1. To do this, we describe explicitly the crystal of the quantum nilpotent subalgebra associated with the translation by the negative of the r-th fundamental weight. Then the crystal can be extended as an affine crystal, in which a certain subcrystal characterized by the εr⁎-statistic is isomorphic to Br,s as an affine crystal, where εr⁎ is also realized precisely in terms of triple and quadruple paths.

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