A Geometric Construction of Crystal Graphs Using Quiver Varieties: Extension to the Non-Simply Laced Case

@article{Savage2005AGC,
  title={A Geometric Construction of Crystal Graphs Using Quiver Varieties: Extension to the Non-Simply Laced Case},
  author={Alistair Savage},
  journal={arXiv: Quantum Algebra},
  year={2005}
}
  • Alistair Savage
  • Published 2005
  • Mathematics
  • arXiv: Quantum Algebra
  • We consider a generalization of the quiver varieties of Lusztig and Nakajima to the case of all symmetrizable Kac-Moody Lie algebras. To deal with the non-simply laced case one considers admissible automorphisms of a quiver and the irreducible components of the quiver varieties fixed by this automorphism. We define a crystal structure on these irreducible components and show that the crystals obtained are isomorphic to those associated to the crystal bases of the lower half of the universal… CONTINUE READING
    17 Citations

    Figures from this paper.

    References

    SHOWING 1-10 OF 23 REFERENCES
    A note on quivers with symmetries
    • 6
    • PDF
    Geometric construction of crystal bases
    • 216
    • PDF
    A geometric realization of spin representations and Young diagrams from quiver varieties
    • 4
    • PDF
    Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
    • 663
    • PDF
    Virtual Crystals and Kleber's Algorithm
    • 40
    • PDF
    Geometric and Combinatorial Realizations of Crystal Graphs
    • 26
    • PDF
    Crystal bases and quiver varieties
    • 47
    • Highly Influential
    Quivers, perverse sheaves, and quantized enveloping algebras
    • 417
    • PDF