Reuven Hodges

activity

20152026

most citedCoxeter combinatorics and spherical Schubert geometry

8 citations · 13 across the 16 of their papers we have counts for

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math.RT2026

Counterexamples to the Reiner-Shimozono conjecture and the failure of Schubert filtrations

Reuven Hodges

We disprove the Reiner--Shimozono conjecture that products of key polynomials have nonnegative expansions in Demazure atoms. By relaxing the defining relations of Demazure modules,…

math.RT2023★ 3 cited

Levi-spherical Schubert varieties

Yibo Gao, Reuven Hodges, Alexander Yong

We prove a short, root-system uniform, combinatorial classification of Levi-spherical Schubert varieties for any generalized flag variety $G / B$ of finite Lie type. We apply this to…

math.RT2020★ 8 cited

Coxeter combinatorics and spherical Schubert geometry

Reuven Hodges, Alexander Yong

For a finite Coxeter system and a subset of its diagram nodes, we define spherical elements (a generalization of Coxeter elements). Conjecturally, for Weyl groups, spherical elemen…

math.RT2018★ 1 cited

A classification of spherical Schubert varieties in the Grassmannian

Reuven Hodges, Venkatramani Lakshmibai

Let $L$ be a Levi subgroup of $G L_{N}$ which acts by left multiplication on a Schubert variety $X (w)$ in the Grassmannian $G_{d, N}$ . We say that $X (w)$ is a spherical Schubert variet…

math.RT2016

Levi Subgroup Actions on Schubert Varieties, Induced Decompositions of their Coordinate Rings, and Sphericity Consequences

Reuven Hodges, Venkatramani Lakshmibai

Let $L_{w}$ be the Levi part of the stabilizer $Q_{w}$ in $G L_{N}$ (for left multiplication) of a Schubert variety $X (w)$ in the Grassmannian $G_{d, N}$ . For the natural action of $L_{w}$ o…