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nLab > Latest Changes: Macdonald polynomial

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  1. typo

    Mamuka Jibladze

    diff, v8, current

    • Wy. Chuang, D-E. Diaconescu, R. Donagi, T. Pantev, Parabolic refined invariants and Macdonald polynomials, Commun. Math. Phys. 335, 1323–1379 (2015) doi

    A string theoretic derivation is given for the conjecture of Hausel, Letellier and Rodriguez-Villegas on the cohomology of character varieties with marked points. Their formula is identified with a refined BPS expansion in the stable pair theory of a local root stack, generalizing previous work of the first two authors in collaboration with Pan. Haiman’s geometric construction for Macdonald polynomials is shown to emerge naturally in this context via geometric engineering. In particular this yields a new conjectural relation between Macdonald polynomials and refined local orbifold curve counting invariants. The string theoretic approach also leads to a new spectral cover construction for parabolic Higgs bundles in terms of holomorphic symplectic orbifolds.

    Škoda Zoran

    diff, v10, current

    • CommentRowNumber3.
    • CommentAuthorzskoda
    • CommentTimeOct 18th 2022

    Doi link corrected doi

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2023

    finally cross-linked poor Ian G. Macdonald with this entry here

    diff, v12, current

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