arXiv subjects

Joseph Baine

Publications and source records attributed to Joseph Baine.

3 recordsLinked to original sources

arXiv2026

The geometry of tilting composition series via Richardson varieties

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.

math.RT↗

arXiv2024

(Co)Minuscule Hecke categories

We determine the p-Kazhdan-Lusztig bases for antispherical (co)minuscule Hecke categories in all characteristics, and for spherical (co)minuscule Hecke categories in good characteristic. This is achieved using geometric and diagrammatic methods. The 2-Kazhdan-Lusztig bases of antispherical cominuscule Hecke categories exhibit extremely pathological behaviour. The notions of p-small resolutions and p-tight elements are introduced and conjecturally explain this behaviour.

math.RT↗

arXiv2024

Monotonicity of inverse Kazhdan-Lusztig polynomials

For arbitrary Coxeter systems, we prove that inverse Kazhdan-Lusztig polynomials satisfy a monotonicity property. This follows from the validity of Soergel's conjecture and the existence of injective morphisms between Rouquier complexes in the mixed perverse Hecke category. The monotonicity property is generalised to parabolic Kazhdan-Lusztig polynomials.

math.RT↗