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Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs

Published 23 Sep 2010 in math.QA and math.RT | (1009.4526v1)

Abstract: We give (conjectural) analogs of Berenstein-Zelevinsky data for affine type $A$. Moreover, by using these affine analogs of Berenstein-Zelevinsky data, we realize the crystal basis of the negative part of the quantized universal enveloping algebra of the (Langlands dual) Lie algebra of affine type $A$.

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