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arXiv · 2601.16937

The geometry of tilting composition series via Richardson varieties

Joseph Baine·Chris Hone
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Abstract

We prove the (graded) Jordan--H\"{o}lder 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.

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Joseph Baine, Chris Hone. 2026-01-23. The geometry of tilting composition series via Richardson varieties. https://arxiv.org/abs/2601.16937

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