Δ–Springer varieties and Hall–Littlewood polynomials

DOI10.1017/fms.2024.1arXiv2209.03503OpenAlexW4391389749MaRDI QIDQ6188340

Sean Griffin

Publication date: 7 February 2024

Published in: Forum of Mathematics, Sigma (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.03503

zbMATH Keywords

cohomologysymmetric functionSpecht modulecoinvariant algebraaffine pavingSpringer fiberordered set partition

Mathematics Subject Classification ID

Partitions of sets (05A18) Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Combinatorial aspects of algebraic geometry (05E14)

Cites Work

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• Cohomology of Spaltenstein varieties
• 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
• Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
• Ordered set partitions, generalized coinvariant algebras, and the delta conjecture
• Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers
• Higher Specht bases for generalizations of the coinvariant ring
• Hilbert schemes, polygraphs and the Macdonald positivity conjecture
• Existence of Affine Pavings for Varieties of Partial Flags Associated to Nilpotent Elements
• The Delta Conjecture
• A flag variety for the Delta Conjecture
• Ordered set partitions, Garsia-Procesi modules, and rank varieties
• Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties

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