On the satake isomorphism

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August undefined, 2024

Web25 de jul. de 2003 · Let G be a general linear group over a local field F. We consider the matrix describing the Satake isomorphism with respect to natural bases. We give a simple proof for the positivity of all matrix coefficients that are not obviously zero. The arguments are elementary and more direct than Rapoport's original proof. WebCoefficient ring of Satake isomorphism. Let G be a split reductive group over local field F, G L be the (complex) Langlands dual group of G. Denote H to be the Z -Hecke algebra of G, that is the ring of G ( O F) -biinvariant Z -valued functions on G ( F). Let R ( G L) be the Grothendieck ring of finite dimensional representation of G L.

ON SATAKE PARAMETERS FOR REPRESENTATIONS WITH …

Web26 de mai. de 2024 · Abstract: We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified $p$-adic group $G$ and generalize the formulation to … WebIn this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a … candylicious edible bubbles

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Web21 de mar. de 2024 · We establish an analogue of the Satake isomorphism for the Hecke algebra of compactly supported, K-biequivariant functions f: G(F) \to End V. These Hecke algebras were first considered by Barthel ... WebIn mathematics, the Satake isomorphism, introduced by Ichirō Satake , identifies the Hecke algebra of a reductive group over a local field with a ring of invariants of the Weyl group. … Web22 de nov. de 2012 · This isomorphism is obtained using the inverse Satake isomorphism constructed in arXiv:1207.5557. We apply this to classify the simple supersingular H_k-modules, study the supersingular block in the category of finite length H_k-modules, and relate the latter to supersingular representations of G. fish wearing glasses

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Webconstruction of the Satake isomorphism, at least in the case that Gis split. The next section will focus on the construction of the Langlands dual group LG, which allows us to generalize Satake’s theorem to the quasi-split case and also formulate Langlands functoriality. Assume now that Gis split (and hence also quasi-split). Web24 de set. de 2008 · of the Satake isomorphism for this algebra, relating it to integrable repre-sentations of the Langlands dual a ne Kac-Moody group. In the next publication we shall use these results to de ne and study the notion of Hecke eigenfunction for the group G a . 1. Introduction 1.1. Langlands duality and the Satake isomorphism. Let F be a global … fish wearing wedding ringWebTraductions en contexte de "anneau du groupe" en français-anglais avec Reverso Context : des moyens permettant d'exciter séparément sur chaque anneau du groupe, des mémoires candylicious houston

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On the satake isomorphism

[1106.3120] Quantum cohomology and the Satake isomorphism

Web2 ALEXANDER KUTZIM AND YIFEI ZHAO Finally, our eld of coe cients is a xed algebraic closure Q ‘ of Q ‘, where ‘is a prime not dividing q.2 For the proof, we will actually consider nite extensions E ⊃Q ‘contained in Q ‘instead, and the Langlands dual group of G will be regarded as a pinned split reductive group G over E. To invoke the Satake … WebAbstract In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper, we give new proofs for some results of that …

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WebAbstract: We consider the matrix for the Satake isomorphism with respect to natural bases. We give a simple proof in the case of Chevalley groups that the matrix coefficients which are not obviously zero are in fact positive numbers. We also relate the matrix coefficients to Kazhdan–Lusztig polynomials and to Bernstein functions. WebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA …

Web2 The Satake Isomorphism The Satake isomorphism is a map between a local Hecke algebra and a ring of symmetric polynomials. In this section we deﬁne the appropriate Hecke algebra, describe the symmetry group corresponding to Spn, and give a few properties of the Satake map. 2.1 Hecke Algebras and Polynomial Rings WebON THE SATAKE ISOMORPHISM. BENEDICT H. GROSS. In this paper, we present an expository treatment of the Satake trans-form. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a local field and the representation ring of the dual group Ĝ. If one wants to use the Satake isomorphism to convert …

WebFind many great new & used options and get the best deals for Galois Representations in Arithmetic Algebraic Geometry by A. J. Scholl: New at the best online prices at eBay! Free shipping for many products! Web27 de mai. de 2024 · In this paper, we give new proofs for some results of that paper, one based on the theory of J -rings and one based on the known character formula for …

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WebThe proof of this proposition is through showing the Satake isomorphism; the reader can consult [8, x4.22-23]. There is an elegant way of reformulating the above proposition, using the Langlands dual group G_ v (for split G v) or the Langlands L-group LG v in general. This reformulation (for split G v for simplicity) is a bijection: fK v-unrami ... fish wearing headphonesWebLet 𝑄 Q italic_Q be the set of all translations in 𝑊 W italic_W, that is the set of all 𝑡 𝑊 t\in W italic_t ∈ italic_W such that the 𝑊 W italic_W -conjugacy class of 𝑡 t italic_t is finite. It is known that 𝑄 … fish wearing sunglassesWeb17 de out. de 2024 · We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on … Expand. 48. PDF. Save. Alert. An introduction to affine Grassmannians and the geometric Satake equivalence. candylicious hong kongWeb10 de dez. de 2013 · The Satake isomorphism allows us to analyze the structure of H (G;K) and hence understand spherical representations. To state the most general … candylicious leioaWebtranslations in W. The classical Satake isomorphism states that the algebra Hsph q is isomorphic to the algebra of W 0-invariants in the group algebra C[Q]. In [L83] we … fish weather forecastWebLet be a reductive algebraic group over a local field or a global field . It is well known that there exists a non-trivial and interesting representation theory of the group as well as the theory of automorphic form… candylicious klccWeb27 de mai. de 2024 · In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper, we give new proofs for some … candylicious hk