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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.16937 |
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| _version_ | 1866915950048051200 |
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| author | Baine, Joseph Hone, Chris |
| author_facet | Baine, Joseph Hone, Chris |
| contents | We prove the (graded) Jordan--Hölder multiplicities of (mixed) tilting sheaves on flag varieties admit a geometric interpretation as the hypercohomology of certain sheaves on Richardson varieties in the Langlands dual flag variety. These sheaves are a motivic variant of geometric extensions, and may be described as a tensor product of parity sheaves on the Schubert and opposite Schubert varieties. We also provide an explicit formula for these multiplicities in terms of $\ell$-Kazhdan--Lusztig polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16937 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The geometry of tilting composition series via Richardson varieties Baine, Joseph Hone, Chris Representation Theory We prove the (graded) Jordan--Hölder multiplicities of (mixed) tilting sheaves on flag varieties admit a geometric interpretation as the hypercohomology of certain sheaves on Richardson varieties in the Langlands dual flag variety. These sheaves are a motivic variant of geometric extensions, and may be described as a tensor product of parity sheaves on the Schubert and opposite Schubert varieties. We also provide an explicit formula for these multiplicities in terms of $\ell$-Kazhdan--Lusztig polynomials. |
| title | The geometry of tilting composition series via Richardson varieties |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.16937 |