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- W2005018763 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a simple finite-dimensional complex Lie algebra with a Cartan subalgebra <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German h> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>h</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {h}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and Weyl group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper W> <mml:semantics> <mml:mi>W</mml:mi> <mml:annotation encoding=application/x-tex>W</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g Subscript n> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathfrak {g}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> denote the Lie algebra of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-jets on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {g}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. A theorem of Raïs and Tauvel and Geoffriau identifies the centre of the category of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German g Subscript n> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>g</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathfrak {g}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-modules with the algebra of functions on the variety of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-jets on the affine space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=German h Superscript asterisk Baseline slash upper W> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=fraktur>h</mml:mi> </mml:mrow> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>W</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathfrak {h}^*/W</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. On the other hand, a theorem of Feigin and Frenkel identifies the centre of the category of critical level smooth modules of the corresponding affine Kac-Moody algebra with the algebra of functions on the ind-scheme of opers for the Langlands dual group. We prove that these two isomorphisms are compatible by defining the higher residue of opers with irregular singularities. We also define generalized Verma and Wakimoto modules and relate them by a nontrivial morphism." @default.
- W2005018763 created "2016-06-24" @default.
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- W2005018763 date "2014-10-03" @default.
- W2005018763 modified "2023-09-27" @default.
- W2005018763 title "Compatibility of the Feigin-Frenkel Isomorphism and the Harish-Chandra Isomorphism for jet algebras" @default.
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- W2005018763 doi "https://doi.org/10.1090/s0002-9947-2014-06419-2" @default.
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