2024 Spherical varieties and langlands duality

Spherical varieties and langlands duality

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August undefined, 2024

Webpaper studies the behavior of global Springer representations under Langlands duality. The main results in [Yun11] on which this paper relies will be reviewed in x1.3. 1.1 Motivations Let Gand G_be almost simple algebraic groups over an algebraic closed eld kwith dual root systems. We call them a pair of Langlands dual groups. 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 …

Quantization and Duality for Spherical Varieties

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 … WebELECTRO-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. i\u0027m a young man after all

Spherical varieties and Langlands duality - CORE Reader

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 … Webthe classi cation of spherical varieties to that of wonderful varieties [11]. Knop proved that G=Hhas a wonderful compacti cation in [7, Corollary 7.6]. We now indicate why the four choices for Labove satisfy (L1) and (L2). If K ... Spherical varieties and Langlands duality, Mosc. Math. J. 10:1 (2010), 65{137. 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. net operating cash flow equation

Quantization and Duality for Spherical Varieties

CiteSeerX — Spherical varieties and 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 ... 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. i\u0027m a year 6 get me out of hereWebadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A i\u0027m a young shot caller

"WebThe de nition of a spherical variety either asks for an open orbit for the Borel subgroup, or it has a multiplicity 1 property for algebraic representations. In the case of G=H, this asks for every irreducible to appear at least once. So this is a nice niteness condition. Examples of spherical varieties are given by the following. " - Spherical varieties and langlands duality

Spherical varieties and langlands duality

Lectures on the Langlands Program and Conformal Field Theory

http://www-personal.umich.edu/~charchan/seminar/ Webquestion to purity of IC sheaves on aﬃne ﬂag varieties. Contents 1. Introduction. 2 1.1. Quantum groups, tilting modules and cohomology. 2 1.2. Koszul duality conjecture. 3 1.3. Plan of the paper. 4 1.4. Notations. 4 1.5. Acknowledgements 5 2. Coherent sheaves: exotic t-structure, and Positivity Lemma. 5 2.1. Exceptional sets and quasi ...

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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. 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 ...

Weblanglands duality spherical variety many aspect finite-dimensional representation perverse sheaf algebraic model affine spherical g-variety certain tensor category dual group loop … WebDec 10, 2006 · Spherical Varieties and Langlands Duality arXiv Authors: Dennis Gaitsgory David Nadler Request full-text Abstract Let G be a connected reductive complex algebraic …

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 … WebNov 10, 2006 · Spherical varieties and Langlands duality D. Gaitsgory, D. Nadler Published 10 November 2006 Mathematics arXiv: Representation Theory Let G be a connected …

WebOur conjectures describe a duality operation on spherical varieties, which exchanges automorphic and spectral quantizations (and may be seen as Langlands duality for …

WebThe 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 ... net operating cash inflowWebJan 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 … i\u0027m a writer not a fighterWebTo 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 net operating cash generated formulaWebNov 10, 2006 · 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... net operating cash outflowWebSpherical 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. … i\u0027m a yummy gummy gummy bearWebIn 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 … net operating income after debt serviceWebHyperspherical 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 … net operating income - debt service