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Using Nakajima’s monomials, we construct a new realization of crystal bases for finite dimensional irreducible modules over quantum classical algebras. We also give an explicit bijection between the… Continue Reading
We give a new realization of the crystal of using generalized Young walls, a modified notion of Young walls of type . Moreover, by the fact that the irreducible highest weight crystal lies in the… Continue Reading
Abstract In this paper, we give a new realization of the crystal B ( ∞ ) using modified Nakajima monomials. For the quantum affine algebras of type A n ( 1 ) , we give an explicit characterization of… Continue Reading
We give a 1-1 correspondence with the Young wall realization and the Young tableau realization of the crystal bases for the classical Lie algebras.
Abstract In this paper, we give an insertion scheme for the tableaux of Kashiwara– Nakashima realizing the crystal bases of the irreducible highest weight modules over the classical Lie algebras. It… Continue Reading
Abstract Zigzag strip bundles are new combinatorial models realizing the crystals B ( ∞ ) for the quantum affine algebras U q ( g ) , where g = B n ( 1 ) , D n ( 1 ) , D n + 1 ( 2 ) , C n ( 1 ) , A 2… Continue Reading
In this article, we give two new realizations of the crystal base B(∞) of the negative part of the quantum generalized Kac–Moody algebra U q (𝔤) (𝔤 =B ∞, C ∞ or D ∞) using Nakajima monomials and… Continue Reading
In this paper, we give a new realization of the crystal basis B(∞) using modified Nakajima monomials for the quantum finite algebras. Moreover, as an application, we obtain the image of the Kashiwara… Continue Reading
In this paper, we give a combinatorial description of the crystal bases of the tensor products of the irreducible highest weight modules over quantum finite algebras in terms of Nakajima monomials.… Continue Reading
ABSTRACT In this article, we give a new realization of crystal bases for irreducible highest weight modules over U q (G 2) in terms of monomials. We also discuss the natural connection between the… Continue Reading