Geometric and Combinatorial Realizations of Crystal Graphs

  title={Geometric and Combinatorial Realizations of Crystal Graphs},
  author={Alistair Savage},
  journal={Algebras and Representation Theory},
  • Alistair Savage
  • Published 20 October 2003
  • Mathematics
  • Algebras and Representation Theory
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… 
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