2 1 N ov 2 00 1 Crystal bases and quiver varieties ( Geometric construction of crystal base II )
نویسنده
چکیده
We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One can show that, as a crystal, it is isomorphic to the crystal base of an irreducible highest weight representation of a quantized universal enveloping algebra.
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...
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