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arXiv · 2504.17430

Stratifying quiver Schur algebras via ersatz parity sheaves

Ruslan Maksimau·Alexandre Minets
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Abstract

We propose an extension of the theory of parity sheaves, which allows for non-locally constant sheaves along strata. Our definition is tailored for proving the existence of (proper, quasihereditary, etc) stratifications of $\mathrm{Ext}$-algebras. We use this to study quiver Schur algebras $A(\alpha)$ for the cyclic quiver of length $2$. We find a polynomial quasihereditary structure on $A(\alpha)$ compatible with the categorified PBW basis of McNamara and Kleshchev-Muth, and sharpen their results to arbitrary characteristic. We also prove that semicuspidal algebras of $A(n\delta)$ are polynomial quasihereditary covers of semicuspidal algebras of the corresponding KLR algebra $R(n\delta)$, and compute them diagrammatically.

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BibTeXRIS

Ruslan Maksimau, Alexandre Minets. 2025-04-24. Stratifying quiver Schur algebras via ersatz parity sheaves. https://arxiv.org/abs/2504.17430

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