The affine description conjecture for subcategories from preprojective quotients

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Suppose that QQ is an affine quiver, let WW be its Weyl group, let Π\Pi be the associated preprojective algebra, and let IwI_w be the ideal associated to w∈Ww\in W. Let Z\mathcal Z be a full subcategory of kQkQ-modules. Affine description conjecture. The subcategory Z\mathcal Z arises as C(Π/Iw)\mathscr{C}(\Pi/I_w) for some w∈Ww\in W if and only if it has finitely many indecomposables, it is subclosed, and, for every tube, at least one ray in the tube does not intersect Z\mathcal Z. The conjecture proposes a precise characterization in the affine case, while the paper presents it as conjectural beyond the cases established earlier.

References

Primary source

Steffen Oppermann, Idun Reiten and Hugh Thomas, “Quotient closed subcategories of quiver representations”, arXiv:1205.3268 (2014).

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