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arXiv · 1702.07570

Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions

Christof Geiß·Bernard Leclerc·Jan Schröer
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Abstract

We generalize Lusztig's nilpotent varieties, and Kashiwara and Saito's geometric construction of crystal graphs from the symmetric to the symmetrizable case. We also construct semicanonical functions in the convolution algebras of generalized preprojective algebras. Conjecturally these functions yield semicanonical bases of the enveloping algebras of the positive part of symmetrizable Kac-Moody algebras.

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Christof Geiß, Bernard Leclerc, Jan Schröer. 2017-02-24. Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions. https://doi.org/10.1007/s00029-018-0412-4

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