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arXiv · 1606.01876

Quiver varieties and crystals in symmetrizable type via modulated graphs

Vinoth Nandakumar·Peter Tingley
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Abstract

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.

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BibTeXRIS

Vinoth Nandakumar, Peter Tingley. 2016-06-06. Quiver varieties and crystals in symmetrizable type via modulated graphs. https://arxiv.org/abs/1606.01876

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