Elementary construction of canonical bases, foldings, and piecewise linear bijections

2025/01/22 by Toshiaki Shoji, Shoji, Toshiaki, Zhiping Zhou +1
Engineering · Mathematics · #17B37 #81R50 #FOS: Mathematics #Mathematics and Applications #Quantum Algebra (math.QA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2501.12568

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbf U_q^- be the negative half of a quantum group of finite type. We construct the canonical basis of \mathbf U_q^- by applying the folding theory of quantum groups, and piecewise linear parametrization of canonical basis. Our construction is elementary, in the sense that we don't appeal to Lusztig's geometric theory of canonical bases, nor to Kashiwara's theory of crystal bases.

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