On the satake isomorphism

WebSatake isomorphism1, which describes the ring of GLn(O)-bi-invariant functions on GLn(F), is the starting point of the Langlands duality. It turns out that the Satake isomorphism admits a vast generalisation, known as the geometric Satake equivalence. This is the starting point of the geometric Langlands program, and

Relative Aspects in Representation Theory, …

WebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … 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 … curbsiders anxiety podcast https://ugscomedy.com

(PDF) ON THE SATAKE ISOMORPHISM - ResearchGate

Webopen subgroup Ke ⊂ G(F) and where a Satake isomorphism is established for the Hecke algebra He K. 1. Introduction The Satake isomorphism plays an important role in automorphic forms and in representation theory of p-adic groups. For global applications, one may often work with unramified groups. We begin by recalling the Satake … 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. 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 ... easy drawing art for kids

ON THE SATAKE ISOMORPHISM - ResearchGate

Category:Introduction - ResearchGate

Tags:On the satake isomorphism

On the satake isomorphism

The Satake Isomorphism and the Langlands Dual - Zachary Gardner

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 ... 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 ...

On the satake isomorphism

Did you know?

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 · 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 ...

Web23 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: … 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 …

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 … 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. …

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 …

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 … easy drawing anime cat boyWeb暨南大学,数字图书馆. 开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 curbside recyclingWebFind 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! curbside recycling asheville ncWebhere. 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) = … curbsiders cme creditWebOn 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: curbside pick up walmart minocquaWeb29 de jul. de 2013 · proof of the Satake isomorphism and encouraging m e to prov e the Casselman-Shalika form ula. I am most grateful to Joseph Berns te in for his attention. and his help in formulating the main result. curbside rewards omaha neWeb22 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. easy drawing for 1st class