. R T ] 2 2 Ja n 20 05 GEOMETRIC AND COMBINATORIAL REALIZATIONS OF CRYSTAL GRAPHS
نویسنده
چکیده
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrary level, describing a combinatorial realization of the crystals in terms of new objects which we call Young pyramids.
منابع مشابه
ar X iv : m at h / 03 10 31 4 v 2 [ m at h . R T ] 1 6 N ov 2 00 3 GEOMETRIC AND COMBINATORIAL REALIZATIONS OF CRYSTAL GRAPHS
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrar...
متن کاملar X iv : m at h / 03 10 31 4 v 3 [ m at h . R T ] 1 9 A ug 2 00 4 GEOMETRIC AND COMBINATORIAL REALIZATIONS OF CRYSTAL GRAPHS
For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrar...
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For irreducible integrable highest weight modules of the finite and affine Lie algebras of type A and D, we define an isomorphism between the geometric realization of the crystal graphs in terms of irreducible components of Nakajima quiver varieties and the combinatorial realizations in terms of Young tableaux and Young walls. For type A (1) n , we extend the Young wall construction to arbitrar...
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