Irreducible modules over Khovanov-Lauda-Rouquier algebras of type An and semistandard tableaux

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Abstract

Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras R and their cyclotomic quotients Rλ of type An. Our construction is compatible with crystal structure. Let B(λ) and B(λ) be the Uq(sln+1)-crystal consisting of marginally large tableaux and semistandard tableaux of shape λ, respectively. On the other hand, let B(λ) and B(λ) be the Uq(sln+1)-crystals consisting of isomorphism classes of irreducible graded R-modules and Rλ-modules, respectively. We show that there exist explicit crystal isomorphisms φ∞:B(∞)→~B(λ) and φ∞:B(λ)→~B(λ). © 2011 Elsevier Inc.

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Kang, S. J., & Park, E. (2011). Irreducible modules over Khovanov-Lauda-Rouquier algebras of type An and semistandard tableaux. Journal of Algebra, 339(1), 223–251. https://doi.org/10.1016/j.jalgebra.2011.05.013

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