49 research outputs found

    Polyhedral realization of Crystal bases for Generalized Kac-Moody Algebras

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    In this paper, we give polyhedral realization of the crystal B()B(\infty) of Uq(g)U_q^-(\mathfrak g) for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of rank 2, 3 and {\it Monster Lie algebras}.Comment: 20 page

    Monomial Relization of Crystal Bases for Special Linear Lie Algebras

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    We give a new realization of crystal bases for finite dimensional irreducible modules over special linear Lie algebras using the monomials introduced by H. Nakajima. We also discuss the connection between this monomial realization and the tableau realization given by Kashiwara and Nakashima.Comment: 15 page

    Young Wall Realization of Crystal Bases for Classical Lie Algebras

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    In this paper, we give a new realization of crystal bases for finite dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight vectors.Comment: 27page

    Nakajima monomials, Young walls and Kashiwara embedding for Uq(An(1))

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    AbstractIn this paper, we realize the crystal basis B(λ) of the irreducible highest weight module V(λ) of level 1 for Uq(An(1)) using Nakajima monomials satisfying some conditions. Also, from this monomial realization, we obtain the image of Kashiwara embedding Ψιλ:B(λ)↪Z∞⊗Rλ, where ι is some infinite sequence from the index set of simple roots. Finally, we give a Uq(An(1))-crystal isomorphism between Young wall realization and monomial realization, and so we can understand the image of Kashiwara embedding Ψιλ:B(λ)↪Z∞⊗Rλ using the combinatorics of Young walls
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