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arXiv · 1605.04266

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

Sean Clark
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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.

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Sean Clark. 2016-05-13. Canonical bases for the quantum enveloping algebra of gl(m|1) and its modules. https://arxiv.org/abs/1605.04266

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