Stratifying quiver Schur algebras via ersatz parity sheaves
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911193587777536 |
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| author | Maksimau, Ruslan Minets, Alexandre |
| author_facet | Maksimau, Ruslan Minets, Alexandre |
| contents | 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 $A(α)$ for the cyclic quiver of length $2$. We find a polynomial quasihereditary structure on $A(α)$ 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 $A(nδ)$ are polynomial quasihereditary covers of semicuspidal algebras of the corresponding KLR algebra $R(nδ)$, and compute them diagrammatically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stratifying quiver Schur algebras via ersatz parity sheaves Maksimau, Ruslan Minets, Alexandre Representation Theory Algebraic Geometry Quantum Algebra 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 $A(α)$ for the cyclic quiver of length $2$. We find a polynomial quasihereditary structure on $A(α)$ 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 $A(nδ)$ are polynomial quasihereditary covers of semicuspidal algebras of the corresponding KLR algebra $R(nδ)$, and compute them diagrammatically. |
| title | Stratifying quiver Schur algebras via ersatz parity sheaves |
| topic | Representation Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2504.17430 |