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- W1996810414 abstract "The present paper studies the connection between the category of modules over the affine Kac-Moody Lie algebra at the critical level, and the category of D-modules on the affine flag scheme <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G left-parenthesis left-parenthesis t right-parenthesis right-parenthesis slash upper I> <mml:semantics> <mml:mrow> <mml:mi>G</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>I</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>G((t))/I</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper I> <mml:semantics> <mml:mi>I</mml:mi> <mml:annotation encoding=application/x-tex>I</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the Iwahori subgroup. We prove a localization-type result, which establishes an equivalence between certain subcategories on both sides. We also establish an equivalence between a certain subcategory of Kac-Moody modules, and the category of quasi-coherent sheaves on the scheme of Miura opers for the Langlands dual group, thereby proving a conjecture of the authors in 2006." @default.
- W1996810414 created "2016-06-24" @default.
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- W1996810414 date "2009-11-02" @default.
- W1996810414 modified "2023-09-24" @default.
- W1996810414 title "D-modules on the affine flag variety and representations of affine Kac-Moody algebras" @default.
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- W1996810414 doi "https://doi.org/10.1090/s1088-4165-09-00360-4" @default.
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