On the satake isomorphism

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August undefined, 2024

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 ... 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 …

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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 … WebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … how is war supposed to be ended

ON THE SATAKE ISOMORPHISM SpringerLink

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 WebAbstract 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 … 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 ... how is washing soda obtained from baking soda

On the satake isomorphism

An introduction to afﬁne Grassmannians and the geometric Satake ...

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 ... 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 …

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WebSATAKE ISOMORPHISM FOR SPECIAL MAXIMAL PARAHORICS 265 such G was described by Cartier [Car], but it is less explicit than that above. It identiﬁesH K withtheringoffunctions C[M(F)/M(F)1]W,whereM:=Cent G(A)isaminimalF-LevisubgroupofGandM(F)1 istheunique maximal compact open subgroup of M(F).The … http://math.stanford.edu/~conrad/JLseminar/Notes/L4.pdf

Web1 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 ... 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!

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 … 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).

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 …

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… how is washington l\u0026i calculatedWebSo 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 is washington dc governedWebcompact 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. how is washington dc defendedWeb24 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 … how is washington dc dividedWeb27 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 … how is waste activated sludge generatedWeb27 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 … how is washi paper madeWebTwisted 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 ... how is waste calculated