Document Type

Article

Publication Date

2018

Publication Title

Mathmetical Research Letters

Volume

25

Pages

159-180

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.

Comments

Author Posting. © International Press of Boston 2018. This article is posted here by permission of the International Press of Boston for personal use, not for redistribution. The article was published in Mathematical Research Letters, 2018, http://dx.doi.org/10.4310/MRL.2018.v25.n1.a7

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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