Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures

zbMath1384.05172arXiv1611.07474MaRDI QIDQ1745187

Benjamin J. Young, Katie Gedeon, Nicholas J. Proudfoot

Publication date: 20 April 2018

Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.07474

zbMATH Keywords

matroidssymmetric functionsreal rootednessKazhdan-Lusztig theory

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Combinatorial aspects of representation theory (05E10) Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items (12)

A combinatorial formula for Kazhdan-Lusztig polynomials of sparse paving matroids ⋮ The Equivariant Inverse Kazhdan--Lusztig Polynomials of Uniform Matroids ⋮ Kazhdan-Lusztig polynomials of fan matroids, wheel matroids, and whirl matroids ⋮ Matroid relaxations and Kazhdan-Lusztig non-degeneracy ⋮ The log-concavity of Kazhdan-Lusztig polynomials of thagomizer matroids ⋮ A combinatorial formula for of \(\rho\)-removed uniform matroids ⋮ The log-concavity of Kazhdan-Lusztig polynomials of uniform matroids ⋮ The Kazhdan-Lusztig polynomials of uniform matroids ⋮ The inverse Kazhdan-Lusztig polynomial of a matroid ⋮ Stirling numbers in braid matroid Kazhdan-Lusztig polynomials ⋮ The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials ⋮ Equivariant Kazhdan-Lusztig polynomials of thagomizer matroids

Uses Software

• SageMath
• OEIS

Cites Work

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• The Hodge theory of Soergel bimodules.
• Representations of Coxeter groups and Hecke algebras
• \(P\)-kernels, IC bases and Kazhdan-Lusztig polynomials
• FI-modules and stability for representations of symmetric groups
• The equivariant Kazhdan-Lusztig polynomial of a matroid
• Kazhdan-Lusztig polynomials of thagomizer matroids
• Representation theory and homological stability.
• The Kazhdan-Lusztig polynomial of a matroid
• Gröbner methods for representations of combinatorial categories
• Hodge Theory of Matroids
• Subdivisions and Local h-Vectors
• Intersection cohomology of the symmetric reciprocal plane

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