Ordered set partitions, Garsia-Procesi modules, and rank varieties

DOI10.1090/tran/8237zbMath1459.05340arXiv2004.00788OpenAlexW3044163819MaRDI QIDQ5853485

Sean Griffin

Publication date: 10 March 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.00788

zbMATH Keywords

symmetric functioncoinvariant algebraSpringer fiberrank varietyordered set partition

Mathematics Subject Classification ID

Partitions of sets (05A18) Combinatorial identities, bijective combinatorics (05A19) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Combinatorics of partially ordered sets (06A07) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40)

Related Items (8)

Set superpartitions and superspace duality modules ⋮ Higher Specht bases for generalizations of the coinvariant ring ⋮ Fermionic diagonal coinvariants and exterior Lefschetz elements ⋮ Springer fibers and the delta conjecture at \(t=0\) ⋮ Δ–Springer varieties and Hall–Littlewood polynomials ⋮ Springer fibers and the Delta Conjecture at \(t = 0\) ⋮ Macdonald polynomials and cyclic sieving ⋮ Cyclic sieving and orbit harmonics

Cites Work

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• A combinatorial approach to the \(q,t\)-symmetry relation in Macdonald polynomials
• The equations of conjugacy classes of nilpotent matrices
• Defining ideals of the closures of the conjugacy classes and representations of the Weyl groups
• An extension of MacMahon's equidistribution theorem to ordered multiset partitions
• Symmetric functions, conjugacy classes and the flag variety
• On certain graded \(S_ n\)-modules and the \(q\)-Kostka polynomials
• Trigonometric sums, Green functions of finite groups and representations of Weyl groups
• A construction of representations of Weyl groups
• A specialization theorem for certain Weyl group representations and an application to the Green polynomials of unitary groups
• On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory.
• Ordered set partitions, generalized coinvariant algebras, and the delta conjecture
• A combinatorial formula for the character of the diagonal coinvariants
• Ordered set partitions, Tanisaki ideals, and rank varieties
• FI-modules and stability for representations of symmetric groups
• Line configurations and \(r\)-Stirling partitions
• Higher Specht bases for generalizations of the coinvariant ring
• Singularities of Generalized Richardson Varieties
• Linear conditions imposed on flag varieties
• Ribbon tableaux, Hall–Littlewood functions, quantum affine algebras, and unipotent varieties
• The Delta Conjecture
• The geometry and combinatorics of Springer fibers
• A combinatorial formula for Macdonald polynomials
• A flag variety for the Delta Conjecture
• Lie Group Representations on Polynomial Rings
• Harmonic bases for generalized coinvariant algebras
• On the singularity of the irreducible components of a Springer fiber in \({\mathfrak{s}\mathfrak{l}_n}\)

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