Geometric and Combinatorial Realizations of Crystal Graphs |
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Authors: | Alistair Savage |
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Institution: | (1) Department of Mathematics, Bahen Centre for Information Technology, University of Toronto, 40 St. George St., Room 6290, Toronto, Ontario, M5S 2E4, Canada |
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Abstract: | 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 An(1), 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.
Presented by P. Littleman
Mathematics Subject Classifications (2000) Primary 16G10, 17B37.
Alistair Savage: This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada
and was partially conducted by the author for the Clay Mathematics Institute. |
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Keywords: | affine Lie algebras Lusztig's quiver variety Nakajima's quiver variety crystal graphs Young tableaux |
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