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

2010/09/23 by Satoshi Naito, Naito, Satoshi, Daisuke Sagaki +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1009.4526

openalex publication_date 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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