A geometric realization of the principal block of quantum group modules at roots of unity is established as microsheaves on an affine Springer fiber, together with a wild-ramification geometric Langlands equivalence to coherent sheaves on the dual Springer resolution.
Modular affine Hecke category and regular unipotent centralizer
2 Pith papers cite this work. Polarity classification is still indexing.
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Characterizes kernel of Iwahori-Whittaker averaging microlocally, generalizes anti-temperedness equivalence theorem, and extends tilting property of central sheaves to integer coefficients.
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Affine Springer fiber and the small quantum group
A geometric realization of the principal block of quantum group modules at roots of unity is established as microsheaves on an affine Springer fiber, together with a wild-ramification geometric Langlands equivalence to coherent sheaves on the dual Springer resolution.
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The tilting property of Whittaker averaged central sheaves
Characterizes kernel of Iwahori-Whittaker averaging microlocally, generalizes anti-temperedness equivalence theorem, and extends tilting property of central sheaves to integer coefficients.