Spherical varieties and langlands duality

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August undefined, 2024

WebToric and ﬂag varieties are both examples of spherical varieties (as expected). Spherical varieties are intimately related to the Langlands program (both geometric and arithmetic). Executive summary: classically one studies automorphic forms on the upper half-plane by calculating period integrals. Now one would like to generalize this, and ... WebJan 24, 2004 · LANGLANDS DUALITY AND ALGEBRAIC GROUPS] 97 let Rep Gˇ k stand for the category of k-representations of Gˇ k; here Gˇ denotes the canonical smooth split reductive group scheme over k whose root datum is dual to that of G. The goal of this paper is to prove the following: (1.1) The categories PG O (Gr,k) and Rep Gˇ k are equivalent as …

Higgs Bundles, Branes and Langlands Duality SpringerLink

WebFeb 6, 2024 · The gerbe of Higgs bundles. Transform Groups 7, 109–153 (2002) Article MathSciNet MATH Google Scholar. Donagi R., Pantev T.: Langlands duality for Hitchin systems. Invent Math. 189, 653–735 (2012) Article ADS MathSciNet MATH Google Scholar. Faltings G.: Stable G -bundles and projective connections. J. WebSpherical varieties and Langlands duality - CORE Reader custom battles url

Spherical Varieties and Langlands Duality - ResearchGate

WebOur conjectures describe a duality operation on spherical varieties, which exchanges automorphic and spectral quantizations (and may be seen as Langlands duality for … WebSpherical varieties and Langlands duality Gaitsgory, D. ; Nadler, D. Let $G$ be a connected reductive complex algebraic group. This paper is devoted to the space $Z$ of … WebIt has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. chasity rosales

Spherical varieties and Langlands duality - CORE Reader

WebJun 19, 2013 · We expect that this smoothness criterion holds for arbitrary spherical varieties. Keywords. horospherical variety arc space motivic integration stringy invariant. MSC classification. ... Gaitsgory, D. and Nadler, D., Spherical varieties and Langlands duality, Mosc. Math. J. 10 ... WebIn the current proposal the PI proposes to develop an analog of several aspects of the so-called Langlands duality to affine Kac-Moody groups. More specifically, the PI proposes to study the spherical and Iwahori Hecke algebras for affine Kac-Moody groups as well as their geometric versions (some parts of that program have already been ... custom battle royaleWebIn an ongoing project of D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at establishing their conjecture in the case of symmetric varieties (an important class of spherical varieties). A key ingredient is … chasity romeo

"WebSPHERICAL VARIETIES AND LANGLANDS DUALITY DENNIS GAITSGORY AND DAVID NADLER Abstract. Let G be a connected reductive complex algebraic group. This paper is … " - Spherical varieties and langlands duality

Spherical varieties and langlands duality

Local L-factors and geometric asymptotics for spherical varieties

WebTo an arbitrary aﬃne spherical G-variety X, one may associate a horospherical variety Xhoro. Its associated subgroup Hˇhoro turns out to be a maximal torus in the subgroup Hˇ associated to X. 2000 Mathematics Subject Classiﬁcation: 22E67, 14M17 Keywords and Phrases: Loop spaces, spherical varieties, Langlands duality WebSep 3, 2010 · Spherical Hall algebras of a weighted projective curve. ... Let H sph ⊂ H f in be the subalgebra generated by K and the characteristic functions 1 vec 1,d and 1 0,d of the connected components ...

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WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical G-variety X. The space Z may be thought of as an algebraic model for the loop space of X. The theory we develop … WebMentioning: 41 - Let G be a connected reductive complex algebraic group. This paper is devoted to the space Z of meromorphic quasimaps from a curve into an affine spherical …

http://www.bvans.net/owr_1305.pdf WebFeb 17, 2024 · Keywords: Spherical variety, Langlands dual group, root system, algebraic group, reductive group

WebThe point is that spherical varieties have good combinatorics: they have now been classi ed (over C) in a way analogous to the classi cation of split reductive groups via root datum. … WebSep 10, 2011 · We can view this isomorphism as a version of the geometric Langlands duality in the formal neighborhood of the trivial local system, for the group GL r . We …

WebFrom two di erent sources, one expects a certain S-duality on the set of hyperspher-ical varieties (this duality acts on the groups involved as well). First, this comes from the S-duality of boundary conditions in N= 4 super Yang-Mills theory [10,11]. Second, this comes from the relative Langlands duality [2]; for a trailer see [1] or [3, §1.7].

WebNov 4, 2024 · To a spherical -variety , one associates a dual group and an -value (encoded in a representation of ), which conjecturally describe the local and automorphic spectra of the variety. This sets up a problem of functoriality, for any morphism of dual groups. We review, and generalize, Langlands' "beyond endoscopy" approach to this problem. chasity royWebSpherical varieties are algebraic varieties equipped with an action of a certain type of algebraic group G subject to a ﬁniteness condition. The type of G will be called reductive. … chasity rossWebELECTRO-MAGNETIC DUALITY AND GEOMETRIC LANGLANDS DUALITY 3 1.1.2. New perspectives. (1) Prediction of elements of the geometric Langlands program for surfaces. This is the most exciting aspect as mathematicians have not been making much progress on this question, at least until the recent work of Braverman and Finkel-berg. chasity romanWebHyperspherical varieties Microlocal perspective: focus on M = T /X /g not X. a ne Hamiltonian variety G M !g ishyperspherical2 if O(M)G is Poisson commutative. Require G … chasity rosenbaumWebThe spherical Hecke algebra for an arbitrary reductive group 56 5.2. Satake isomorphism 57 5.3. The Langlands correspondence for an arbitrary reductive group 59 ... the Langlands duality is indeed closely related to the S-duality of quantum eld theory, and this opens up exciting possibilities for both subjects. The goal of these notes is two ... custom battle rules pokemon showdown chasity rogers south carolina vetWebadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A custom battle royale apex