Every rectangular semistandard Young tableau induces a positroidal subdivision of the hypersimplex, and for Gr(2,n) the non-frozen prime tableaux are exactly the coarsest such subdivisions.
Classification of prime modules of quantum affine algebras corresponding to 2-column tableaux
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abstract
Finite dimensional simple modules of quantum affine algebras of type A correspond to semistandard Young tableaux of rectangular shapes. In this paper, we classify all prime modules corresponding to 2-column semistandard Young tableaux, up to a conjectural property. Moreover, we give a conjectural sufficient condition for a module corresponding to a tableau with more than two columns to be prime.
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From dual canonical bases to positroidal subdivisions
Every rectangular semistandard Young tableau induces a positroidal subdivision of the hypersimplex, and for Gr(2,n) the non-frozen prime tableaux are exactly the coarsest such subdivisions.