English

Monomial bases and canonical bases for quantum affine algebras

Quantum Algebra 2026-05-19 v2

Abstract

We construct a monomial basis of a quantum affine algebra of simply-laced type, associated to the PBW basis of Beck-Nakajima. We show that there exists a simple algorithm of computing canonical basis in terms of the monomial basis. We dsicuss the relations of the canonical basis obtained from this PBW basis with Lusztig's canonical basis constructed by using the geometry of quivers.

Keywords

Cite

@article{arxiv.2605.14247,
  title  = {Monomial bases and canonical bases for quantum affine algebras},
  author = {Toshiaki Shoji and Zhiping Zhou},
  journal= {arXiv preprint arXiv:2605.14247},
  year   = {2026}
}

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40 pages