On the satake isomorphism

WebLet 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… WebThe Satake isomorphism is a map H(G;K) !H(M;oM) de ned by sending f2H(G;K) to the function Sf, de ned by (Sf)(m) = (m)1=2 Z N f(mn)dn= (m) 1=2 Z N f(nm)dm: This …

GEOMETRIC SATAKE, SPRINGER CORRESPONDENCE, AND SMALL …

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 … 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 … northland school division website https://digitalpipeline.net

ON SATAKE PARAMETERS FOR REPRESENTATIONS WITH …

Web1 de dez. de 2024 · Abstract: In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper we give new proofs for … WebOn Matrix Coe cients of the Satake Isomorphism 3 reduced expression of a xed ˝). Denote by G(˝) the set f˙k j f˙jgk j=0 2 Gg. We will use the following result of Dabrowski: 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). how to say story in french

Coefficient ring of Satake isomorphism - MathOverflow

Category:ON THE SATAKE ISOMORPHISM - R Discovery

Tags:On the satake isomorphism

On the satake isomorphism

检索结果-暨南大学图书馆

Webtranslations 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 … Webcompact subgroup of G(F), and the Satake isomorphism in [HRo] coincides with the classical one described by Cartier [Car]. In this case ˇ7!s(ˇ) agrees with the usual Satake parameter for unrami ed groups which is described in [Bor]. In the general quasi-split case, the main complication is due to the disconnectedness of the reductive group GbI F.

On the satake isomorphism

Did you know?

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 … 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

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 … Web27 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 …

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 … Web27 de mai. de 2024 · Download Citation ON THE SATAKE ISOMORPHISM In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke …

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 ...

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 northland school divisionWeb1 de dez. de 2024 · Download Citation On the Satake isomorphism In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras with equal parameters. In this paper we ... how to say story in spanishWeb20 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 … northland school division 69Web15 de jun. de 2011 · Quantum cohomology and the Satake isomorphism. We prove that the geometric Satake correspondence admits quantum corrections for minuscule … how to say strainer in italianWeb27 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 results of that paper, one based on the ... how to say stormy in spanishWebIn 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. … how to say stormy in frenchWeb23 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: … northland school division alberta