On the satake isomorphism
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 … 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 …
On the satake isomorphism
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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. WebIn 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 …
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… WebTwisted geometric Satake equivalence. Twisted geometric Satake equivalence. 期刊名称： Journal of the Institute of Mathematics of Jussieu 作者： Finkelberg, Michael,Lysenko, Sergey 年份： 2010年 期号： 第04期 关键词： geometric Langlands program; Satake isomorphism; monodromic perverse sheaves. 内容由中国教育图书 ...
http://www2.math.umd.edu/~tjh//Satake_parameters_v2.pdf 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).
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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. thinking matters podcastWebcompact 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. thinking matters programWeb26 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 … thinking matters schoolWeb24 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 … thinking matters warringtonWebhere. 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) = … thinking meaningWebThe 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 … thinking mediaWebtranslations 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 … thinking meaning in psychology