Categorifications of Non-Integer Quivers: Types 𝐻₄, 𝐻₃ and 𝐼₂(2𝑛+1)

Duffield, Drew; Tumarkin, Pavel

doi:10.1090/ert/671

Categorifications of Non-Integer Quivers: Types $H_4$, $H_3$ and $I_2(2n+1)$
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by Drew Damien Duffield and Pavel Tumarkin;

Represent. Theory 28 (2024), 275-327

DOI: https://doi.org/10.1090/ert/671

Published electronically: August 29, 2024

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Abstract:

We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types $H_4$, $H_3$ and $I_2(2n+1)$. In particular, the (un)folding induces a semiring action on the categories associated to the unfolded quivers of types $E_8$, $D_6$ and $A_{2n}$ respectively. We then define the tropical seed pattern on the folded quivers, which includes $c$- and $g$-vectors, and show its compatibility with the unfolding.

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