Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules

2016/05/13 by Sean Clark, Clark, Sean
Mathematics · Physics and Astronomy · #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1605.04266

openalex publication_date 2016/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct a crystal basis for the negative half of the quantum group U associated to the standard super Cartan datum of gl(m|1), which is compatible with known crystals on Kac modules and simple modules. We show that these crystals admit globalization functions which produce compatible canonical bases. We then define a braid group action on a family of quantum groups including U, and use this action to show that our canonical basis agrees with those constructed from PBW bases. Finally, we explicitly compute some small-rank examples.

Citations

• A categorification of the positive half of quantum gl(m|1)

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