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Nil-Brauer categorifies the split iquantum group of rank one

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arxiv 2305.05877 v2 pith:ROLO5MXG submitted 2023-05-10 math.QA math.RT

Jonathan Brundan , Weiqiang Wang , Ben Webster This is my paper · ORCID
classification math.QAmath.RT
keywords gradedmodulescategorygroupiquantumnil-brauerprojectiverank
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We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the split iquantum group of rank one. Under this isomorphism, the indecomposable graded projective modules correspond to the icanonical basis. We also derive character formulae for irreducible graded modules and deduce various branching rules.

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  1. Categorification of quasi-split iquantum groups

    math.QA 2025-05 accept novelty 8.0 of 10

    New diagram 2-categories are defined whose Grothendieck rings are proved isomorphic to the integral forms of quasi-split iquantum groups for symmetric Cartan types, yielding new bases and a new proof of the Balagović-...

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