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Quantum loop groups and critical convolution algebras

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arxiv 2302.01418 v5 pith:H5ICC5R4 submitted 2023-02-02 math.RT

classification math.RT
keywords algebrascriticalattachedconvolutionfamilygroupsloopquantum
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We realize geometrically a family of simple modules of (shifted) quantum loop groups including Kirillov-Reshetikhin and prefundamental representations. To do this, we introduce a new family of algebras attached to quivers with potentials, using critical K-theory and critical Borel-Moore homology, which generalizes the convolution algebras attached to quivers defined by Nakajima.

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