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On the satake isomorphism

Web20 de jul. de 2014 · Instead, we prove that, if the derived subgroup of \( { \mathrm G}\) is simply connected, our isomorphism is an inverse to the Satake transform of . We give … WebLet 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 …

Satake isomorphism - Wikipedia

Webisomorphism on each of these components. In other types, the map ˇis slightly more complicated, but its bres and its image are described explicitly in [AH]. The present paper focuses on the representation-theoretic implications of this map ˇ. Consider these four functors (which will be de ned fully in Section 2): The geometric Satake ... 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. bitter breakup with gas stoves https://roosterscc.com

Unramified representations and the Satake isomorphism

WebTraductions 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 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). 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. datasheet flyback transformer

An inverse Satake isomorphism in characteristic \(p\) - Springer

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On the satake isomorphism

THE SATAKE ISOMORPHISM FOR SPECIAL MAXIMAL …

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. … Web23 de ago. de 2010 · We establish an analogue of the Satake isomorphism for the Hecke algebra of compactly supported, K -biequivariant functions f: G ( F )→End V. These …

On the satake isomorphism

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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 … WebSo the Satake transform captures the action of H(G,K 0) on unramified principal series representations. Theorem 1.3. The Satake theorem is a C-algebra homomorphism which …

Web10 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 … 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 …

Webhere. What we will do is some calculations that suggest the general outline of the proof of Satake’s theorem. Suppose we have a decomposition K ($)K= ‘ i x iK. Since G(F) = … Web9 de jan. de 2002 · Download PDF Abstract: The geometric Satake isomorphism is an equivalence between the categories of spherical perverse sheaves on affine Grassmanian and the category of representations of the Langlands dual group. We provide a similar description for derived categories of l-adic sheaves on an affine flag variety which are …

Web15 de jun. de 2011 · Quantum cohomology and the Satake isomorphism. We prove that the geometric Satake correspondence admits quantum corrections for minuscule …

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! datasheet flyeralarm.comWebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … datasheet flip flop srWebDERIVED SATAKE ISOMORPHISM AND IWAHORI-HECKE ALGEBRAS, [?, x3-4] 5 The reduction map A \K !A splits uniquely, and under our hypotheses induces an isomorphism on cohomology with coe cients in S H(A \K;S) ’H(A;S) Following Venkatesh, we make this identi cation for the remainder. To summarise, for the derived Hecke algebra of a torus … bitter breast-caresWeb2 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 datasheet flow sensorWeb23 de mar. de 2010 · On the Satake isomorphism; By Benedict H. Gross; Edited by A. J. Scholl, University of Durham, R. L. Taylor , Harvard University, Massachusetts; Book: … bitter brew for short crosswordWeb27 de mai. de 2024 · AbstractIn a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper, we give new proofs for … bitter brew briefly crosswordWeb21 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 ... bitter brew book