Combinatorial realizations of crystals via torus actions on quiver varieties

@inproceedings{Sam2014CombinatorialRO,
  title={Combinatorial realizations of crystals via torus actions on quiver varieties},
  author={Steven V. Sam and Peter Tingley},
  year={2014}
}
Let V (λ) be a highest weight representation of a symmetric Kac–Moody algebra, and let B(λ) be its crystal. There is a geometric realization of B(λ) using Nakajima’s quiver varieties. In many particular cases one can also realize B(λ) by elementary combinatorial methods. Here we study a general method of extracting combinatorial realizations from the geometric picture: we use Morse theory to index the irreducible components by connected components of the subvariety of fixed points for a certain… CONTINUE READING

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