FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4311441456> ?p ?o ?g. }

• W4311441456 endingPage "3640" @default.
• W4311441456 startingPage "3585" @default.
• W4311441456 abstract "In a previous paper, the first and third authors gave an explicit realization of the geometric Langlands correspondence for hypergeometric sheaves, considered as <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper G normal upper L Subscript n> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>G</mml:mi> <mml:mi mathvariant=normal>L</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathrm {GL}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-local systems. Certain hypergeometric local systems admit a symplectic or orthogonal structure, which can be viewed as <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-local systems, for a classical group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This article aims to realize the geometric Langlands correspondence for these <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-local systems. We study this problem from two aspects. In the first approach, we define the hypergeometric automorphic data for a classical group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper G> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=application/x-tex>G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in the framework of Yun, one of whose local components is a new class of euphotic representations in the sense of Jakob–Yun. We prove the rigidity of hypergeometric automorphic data under natural assumptions, which allows us to define <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-local systems <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper E Subscript ModifyingAbove upper G With ˇ> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>E</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>mathcal {E}_{check {G}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper G Subscript m> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>G</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathbb {G}_m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as Hecke eigenvalues (in both <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script l> <mml:semantics> <mml:mi>ℓ<!-- ℓ --></mml:mi> <mml:annotation encoding=application/x-tex>ell</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic and de Rham settings). In the second approach (which works only in the de Rham setting), we quantize a ramified Hitchin system, following Beilinson–Drinfeld and Zhu, and identify <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=script upper E Subscript ModifyingAbove upper G With ˇ> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi class=MJX-tex-caligraphic mathvariant=script>E</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> </mml:mrow> </mml:msub> <mml:annotation encoding=application/x-tex>mathcal {E}_{check {G}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with certain <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-opers on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper G Subscript m> <mml:semantics> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>G</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>mathbb {G}_m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Finally, we compare these <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper G With ˇ> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>G</mml:mi> <mml:mo stretchy=false>ˇ<!-- ˇ --></mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding=application/x-tex>check {G}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-opers with hypergeometric local systems." @default.
• W4311441456 created "2022-12-26" @default.
• W4311441456 creator A5028288805 @default.
• W4311441456 creator A5038909759 @default.
• W4311441456 creator A5040714277 @default.
• W4311441456 date "2023-01-27" @default.
• W4311441456 modified "2023-10-05" @default.
• W4311441456 title "Hypergeometric sheaves for classical groups via geometric Langlands" @default.
• W4311441456 cites W1617671828 @default.
• W4311441456 cites W1965149844 @default.
• W4311441456 cites W2028411245 @default.
• W4311441456 cites W2076975228 @default.
• W4311441456 cites W2105889671 @default.
• W4311441456 cites W2120081664 @default.
• W4311441456 cites W2125393842 @default.
• W4311441456 cites W2129442785 @default.
• W4311441456 cites W2561660278 @default.
• W4311441456 cites W2609640769 @default.
• W4311441456 cites W2924713230 @default.
• W4311441456 cites W2962718966 @default.
• W4311441456 cites W2962843244 @default.
• W4311441456 cites W2963558337 @default.
• W4311441456 cites W2963627435 @default.
• W4311441456 cites W2981480068 @default.
• W4311441456 cites W3098557890 @default.
• W4311441456 cites W3101698882 @default.
• W4311441456 cites W3173959784 @default.
• W4311441456 cites W4205234242 @default.
• W4311441456 cites W4247813966 @default.
• W4311441456 cites W4297153798 @default.
• W4311441456 doi "https://doi.org/10.1090/tran/8848" @default.
• W4311441456 hasPublicationYear "2023" @default.
• W4311441456 type Work @default.
• W4311441456 citedByCount "1" @default.
• W4311441456 countsByYear W43114414562022 @default.
• W4311441456 crossrefType "journal-article" @default.
• W4311441456 hasAuthorship W4311441456A5028288805 @default.
• W4311441456 hasAuthorship W4311441456A5038909759 @default.
• W4311441456 hasAuthorship W4311441456A5040714277 @default.
• W4311441456 hasBestOaLocation W43114414562 @default.
• W4311441456 hasConcept C11413529 @default.
• W4311441456 hasConcept C154945302 @default.
• W4311441456 hasConcept C2776321320 @default.
• W4311441456 hasConcept C33923547 @default.
• W4311441456 hasConcept C41008148 @default.
• W4311441456 hasConceptScore W4311441456C11413529 @default.
• W4311441456 hasConceptScore W4311441456C154945302 @default.
• W4311441456 hasConceptScore W4311441456C2776321320 @default.
• W4311441456 hasConceptScore W4311441456C33923547 @default.
• W4311441456 hasConceptScore W4311441456C41008148 @default.
• W4311441456 hasIssue "5" @default.
• W4311441456 hasLocation W43114414561 @default.
• W4311441456 hasLocation W43114414562 @default.
• W4311441456 hasOpenAccess W4311441456 @default.
• W4311441456 hasPrimaryLocation W43114414561 @default.
• W4311441456 hasRelatedWork W1979597421 @default.
• W4311441456 hasRelatedWork W2007980826 @default.
• W4311441456 hasRelatedWork W2218034408 @default.
• W4311441456 hasRelatedWork W2263699433 @default.
• W4311441456 hasRelatedWork W2358755282 @default.
• W4311441456 hasRelatedWork W2361861616 @default.
• W4311441456 hasRelatedWork W2377979023 @default.
• W4311441456 hasRelatedWork W2392921965 @default.
• W4311441456 hasRelatedWork W2748952813 @default.
• W4311441456 hasRelatedWork W2899084033 @default.
• W4311441456 hasVolume "376" @default.
• W4311441456 isParatext "false" @default.
• W4311441456 isRetracted "false" @default.
• W4311441456 workType "article" @default.