8 citations · 13 across the 16 of their papers we have counts for
23 papers
Dot actions and Hessenberg spaces for dihedral groups
Jonathan Boretsky, Reuven Hodges, Nathan Lesnevich +2
Splines on Weyl groups model the equivariant cohomology of regular semisimple Hessenberg varieties, and the natural group action on them encodes the monodromy action. The resulting…
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,…
Kleber's conjecture and complementary products of symmetric functions
Reuven Hodges, Hanzhang Yin
We prove Kleber's rectangular-complement conjecture for Schur functions over an arbitrary commutative ring , showing that, for a fixed rectangle, the products , i…
The record statistic and forward stability of Schubert products
Andrew Hardt, Reuven Hodges, Hanzhang Yin
We initiate a probabilistic study of forward stability for products of Schubert polynomials through the record statistic (left-to-right maxima) of permutations. Building on the exp…
Comparability in Bruhat orders
Jonathan Boretsky, Alvaro Cornejo, Reuven Hodges +3
We determine the sharp asymptotic scale of the probability that two uniformly random permutations are comparable in weak Bruhat order, showing that $\mathbb{P}(σ_1 \preceq_W σ_2)=\…
A non-iterative straightening algorithm and orthogonality for skew Schur modules
Reuven Hodges, Hanzhang Yin
We generalize Fulton's determinantal construction of Schur modules to the skew setting, providing an explicit and functorial presentation using only elementary linear algebra and d…
Kohnert posets and polynomials of northeast diagrams
Aram Bingham, Beth Anne Castellano, Kimberly P. Hadaway +4
Kohnert polynomials and their associated posets are combinatorial objects with deep geometric and representation theoretic connections, generalizing both Schubert polynomials and t…
Orbit structures and complexity in Schubert and Richardson Varieties
Yibo Gao, Reuven Hodges
The goal of this paper is twofold. Firstly, we provide a type-uniform formula for the torus complexity of the usual torus action on a Richardson variety, by developing the notion o…
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 of finite Lie type. We apply this to…
Proper elements of Coxeter groups
József Balogh, David Brewster, Reuven Hodges
We extend the notion of proper elements to all Coxeter groups. For all infinite families of finite Coxeter groups we prove that the probability a random element is proper goes to z…
Equations for GL invariant families of polynomials
Paul Breiding, Christian Ikenmeyer, Mateusz Michałek +1
We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer…
Approximate counting of standard set-valued tableaux
Reuven Hodges, Gidon Orelowitz
We present a randomized algorithm for generating standard set-valued tableaux by extending the Green-Nijenhuis-Wilf hook walk algorithm. In the case of asymptotically rank two part…
Classification of Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong
A Schubert variety in the complete flag manifold is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give…
Proper permutations, Schubert geometry, and randomness
David Brewster, Reuven Hodges, Alexander Yong
We define and study proper permutations. Properness is a geometrically natural necessary criterion for a Schubert variety to be Levi-spherical. We prove the probability that a rand…
Multiplicity-free skew Schur polynomials
Shiliang Gao, Reuven Hodges, Gidon Orelowitz
We provide a non-recursive, combinatorial classification of multiplicity-free skew Schur polynomials. These polynomials are , and , characters of the skew Schur modules…
Multiplicity-free key polynomials
Reuven Hodges, Alexander Yong
The key polynomials, defined by A. Lascoux-M.-P. Schützenberger, are characters for the Demazure modules of type A. We classify multiplicity-free key polynomials. The proof uses tw…
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…
A classification of spherical Schubert varieties in the Grassmannian
Reuven Hodges, Venkatramani Lakshmibai
Let be a Levi subgroup of which acts by left multiplication on a Schubert variety in the Grassmannian . We say that is a spherical Schubert variet…
Toroidal Schubert Varieties
Mahir Bilen Can, Reuven Hodges, Venkatramani Lakshmibai
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the to…
Sphericality and Smoothness of Schubert Varieties
Mahir Bilen Can, Reuven Hodges
We consider the action of the Levi subgroup of a parabolic subgroup that stabilizes a Schubert variety. We show that a smooth Schubert variety is a homogeneous space for a paraboli…
A non-iterative formula for straightening fillings of Young diagrams
Reuven Hodges
Young diagrams are fundamental combinatorial objects in representation theory and algebraic geometry. Many constructions that rely on these objects depend on variations of a straig…
Levi Subgroup Actions on Schubert Varieties, Induced Decompositions of their Coordinate Rings, and Sphericity Consequences
Reuven Hodges, Venkatramani Lakshmibai
Let be the Levi part of the stabilizer in (for left multiplication) of a Schubert variety in the Grassmannian . For the natural action of o…
Free Resolutions of Some Schubert Singularities in the Lagrangian Grassmannian
Venkatramani Lakshmibai, Reuven Hodges
In this paper we construct free resolutions of certain class of closed subvarieties of affine space of symmetric matrices (of a given size). Our class covers the symmetric determin…