What type of study is this?

This is a Quantitative Study study.

October 8, 2025Open Access

Algorithm for computing canonical bases and foldings of quantum groups

Key Points

This research extends existing algorithms for computing the transition matrix of quantum groups.
Antor's algorithm for symmetric quantum groups is adapted to handle non-symmetric cases effectively.
The relationship between the negative half of a quantum group and its non-symmetric counterpart is elucidated.
Key connections between canonical and PBW bases are discussed, enhancing understanding of quantum group structures.

Abstract

Let Uq^- be the negative half of a quantum group of finite type. Let P be the transition matrix between the canonical basis and a PBW basis of Uq^-. In the case Uq^- is symmetric, Antor gave a simple algorithm of computing P by making use of monomial bases. By the folding theory, Uq^- (symmetric, with a certain automorphism) is related to a quantum group Uq^- of non-symmetric type. In this paper, we extend the results of Antor to the non-symmetric case, and discuss the relationship between the algorithms for Uq^- and for Uq^-.

Read Full Paperexternally

Ask AI

Helpful

Bookmark

View Full Paper