Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties
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Publication:5916010
DOI10.1016/j.aim.2018.02.020zbMath1410.05222arXiv1511.00773OpenAlexW2962838937WikidataQ130073891 ScholiaQ130073891MaRDI QIDQ5916010
Timothy Y. Chow, Patrick Brosnan
Publication date: 23 April 2018
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1511.00773
reciprocitychromatic quasisymmetric functionShareshian-Wachs conjectureStanley-Stembridge conjecturelocal invariant cycle theorempalindromicity
Combinatorial aspects of partitions of integers (05A17) Permutations, words, matrices (05A05) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Special varieties (14M99)
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Cites Work
- Unnamed Item
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- Chromatic quasisymmetric functions
- Affine pavings of Hessenberg varieties for semisimple groups
- The Betti numbers of regular Hessenberg varieties are palindromic
- On de Jong's conjecture
- Decomposition theorem for proper Kähler morphisms
- Schubert polynomials and classes of Hessenberg varieties
- Simple singularities and simple algebraic groups
- Singularities and topology of hypersurfaces
- Finiteness of local fundamental groups for quotients of affine varieties under reductive groups
- On a conjecture of Kashiwara.
- On immanants of Jacobi-Trudi matrices and permutations with restricted position
- A symmetric function generalization of the chromatic polynomial of a graph
- Algebraic Geometry. I: Complex projective varieties.
- The path-cycle symmetric function of a digraph
- Incomparability graphs of \((3+1)\)-free posets are \(s\)-positive
- Manifolds, sheaves, and cohomology
- Hitchin fibration and endoscopy
- Local classification of quotients of complex manifolds by discontinuous groups
- Equations différentielles à points singuliers réguliers
- Linear conditions imposed on flag varieties
- Asymptotic behaviour of tame harmonic bundles and an application to pure twistor 𝐷-modules. I
- Asymptotic behaviour of tame harmonic bundles and an application to pure twistor 𝐷-modules. II
- Permutation actions on equivariant cohomology
- Hessenberg Varieties
- Chromatic quasisymmetric functions and Hessenberg varieties
- Hessenberg varieties, intersections of quadrics, and the Springer correspondence
- Hecke Algebra Characters and Immanant Conjectures
- Lie Group Representations on Polynomial Rings
- Mod $\ell$ representations of arithmetic fundamental groups II: A conjecture of A. J. de Jong
- Local Systems and Constructible Sheaves
- The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture
- A conjecture on arithmetic fundamental groups