Mathmetical Research Letters
Kashiwara and Saito have a geometric construction of the infinity crystal for any symmetric Kac–Moody algebra. The underlying set consists of the irreducible components of Lusztig’s quiver varieties, which are varieties of nilpotent representations of a pre-projective algebra. We generalize this to symmetrizable Kac–Moody algebras by replacing Lusztig’s preprojective algebra with a more general one due to Dlab and Ringel. In non-symmetric types we are forced to work over non-algebraically-closed fields.
Nandakumar, Vinoth and Tingley, Peter. Quiver Varieties and Crystals in Symmetrizable Type via Modulated Graphs. Mathmetical Research Letters, 25, : 159-180, 2018. Retrieved from Loyola eCommons, Mathematics and Statistics: Faculty Publications and Other Works, http://dx.doi.org/10.4310/MRL.2018.v25.n1.a7
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