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 … 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 ...
On the satake isomorphism
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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). 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 …
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. 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 ...
WebON THE SATAKE ISOMORPHISM 5 Since we can take xi = λ(π) and yj = µ(π), this shows that nλ,µ(λ+µ) ≥ 1. In fact, we will see later that nλ,µ(λ + µ) = 1 and that nλ,µ(ν) 6= 0 implies that ν ≤(λ+ µ). Therefore (2.9) cλ ·cµ = cλ+µ + X ν<(λ+µ) nλ,µ(ν)·cν The most important … 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 …
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.
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 ... how many parts are in a engineWebhere. 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) = … how can ai help mental healthWeb22 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. how many parts are in a sarWeb21 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 ... how can ai help with climate changeWebSo 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 … how can ai help sustainabilityWeb17 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. how can ai help societyWebIn 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 … how can a indoor cat get worms