Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers

DOI10.4007/annals.2020.192.1.3zbMath1467.14086arXiv1710.04513OpenAlexW3043425435MaRDI QIDQ2193963

Anton Mellit

Publication date: 25 August 2020

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.04513

zbMATH Keywords

Poincaré polynomialsMacdonald polynomialsHall algebrasHiggs bundlescharacter varieties

Mathematics Subject Classification ID

Vector bundles on curves and their moduli (14H60) Character varieties (14M35)

Related Items (14)

Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures) ⋮ Colored fermionic vertex models and symmetric functions ⋮ Intersection cohomology of character varieties for punctured Riemann surfaces ⋮ CHARACTER STACKS ARE PORC COUNT ⋮ \(q\)-Whittaker functions, finite fields, and Jordan forms ⋮ New structures for colored HOMFLY-PT invariants ⋮ On character varieties of singular manifolds ⋮ E-Polynomials of Generic -Character Varieties: Branched Case ⋮ On the cohomology of character stacks for non-orientable surfaces ⋮ Δ–Springer varieties and Hall–Littlewood polynomials ⋮ Motivic Donaldson-Thomas invariants of parabolic Higgs bundles and parabolic connections on a curve ⋮ Unnamed Item ⋮ Quiver representations in abelian categories ⋮ Virtual classes of representation varieties of upper triangular matrices via topological quantum field theories

Cites Work

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• Arithmetic harmonic analysis on character and quiver varieties
• Mixed Hodge polynomials of character varieties. With an appendix by Nicholas M. Katz.
• Counting colorings on varieties
• Higgs bundles and local systems
• On the cohomology groups of moduli spaces of vector bundles on curves
• Compactification of moduli of parabolic sheaves and moduli of parabolic Higgs sheaves
• Integrality of Hausel-Letellier-Villegas kernels
• Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems.
• Absolutely indecomposable representations and Kac-Moody Lie algebras. (With an appendix by Hiraku Nakajima).
• Hall algebras, hereditary algebras and quantum groups
• A remarkable \(q,t\)-Catalan sequence and \(q\)-Lagrange inversion
• Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures)
• On the motives of moduli of chains and Higgs bundles
• Stability conditions on triangulated categories
• Topological mirror symmetry for parabolic Higgs bundles
• Cohomology of large semiprojective hyperkaehler varieties
• Solutions of the Motivic ADHM Recursion Formula
• Harmonic Bundles on Noncompact Curves
• Betti numbers of the moduli space of rank 3 parabolic Higgs bundles
• The Self-Duality Equations on a Riemann Surface
• HOMOLOGICAL ALGEBRA OF TWISTED QUIVER BUNDLES
• A combinatorial formula for Macdonald polynomials
• Generators for the cohomology ring of the moduli space of rank 2 Higgs bundles
• Counting Higgs bundles and type quiver bundles
• On the Rationality of the Zeta Function of an Algebraic Variety
• Indecomposable vector bundles and stable Higgs bundles over smooth projective curves

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