English

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

Representation Theory 2018-11-15 v2 Rings and Algebras

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.

Keywords

Cite

@article{arxiv.1702.07570,
  title  = {Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions},
  author = {Christof Geiß and Bernard Leclerc and Jan Schröer},
  journal= {arXiv preprint arXiv:1702.07570},
  year   = {2018}
}

Comments

50 pages. Version 2: A few typos fixed. Final version published in Selecta Mathematica