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arXiv · 2609.30637

Quasi-equivalence of relabeled positroid cluster structures

Yilin Wu
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Abstract

We prove the Fraser--Sherman-Bennett conjecture on the quasi-equivalence of positroid cluster structures arising from admissibly relabeled plabic graphs. We construct a tilting module from the boundary necklace and obtain a Frobenius categorification of the relabeled cluster structure. By identifying localized characters of rank-one modules with Plücker coordinates, we match the stable images of the mutable face modules with the summands of a reachable cluster-tilting object in the stable category. The induced derived equivalence yields a unimodular transformation of relative index lattices intertwining the full extended exchange matrices. These comparisons show that the identity map on the coordinate ring is a quasi-cluster isomorphism between the two cluster structures.

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Yilin Wu. 2026-10-16. Quasi-equivalence of relabeled positroid cluster structures. https://arxiv.org/abs/2609.30637

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