On the satake isomorphism

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August undefined, 2024

http://math.stanford.edu/~conrad/JLseminar/Notes/L4.pdf 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 …

OBERSEMINAR: SHTUKAS FOR REDUCTIVE GROUPS AND GLOBAL …

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 … Web27 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 … chitear

On the Satake isomorphism - ResearchGate

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 … WebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … grap on operating leases

The Satake Isomorphism and the Langlands Dual - Zachary Gardner

On The Satake Isomorphism: Benedict H. Gross PDF Topology …

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 ... 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 … gra pow pbj thumbprintWeb21 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 ... chi tea burger

"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. … " - On the satake isomorphism

On the satake isomorphism

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: 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

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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 …

WebIn this paper, we present an expository treatment of the Satake transform. This gives an isomorphism between the spherical Hecke algebra of a split reductive group G over a … 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 ...

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 … 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 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 …

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 ... chi tea is actually good for youWebBegins with an article on the geometric Satake isomorphism, a key theorem in the geometric Langlands program. Part of the book series: Lecture Notes in ... Starting with a very detailed article by P. Baumann … grap on traffic finesWebFind 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! grapow fried riceWeb23 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 … grapnur the crusherWebAbstract: We consider the matrix for the Satake isomorphism with respect to natural bases. We give a simple proof in the case of Chevalley groups that the matrix coefficients which are not obviously zero are in fact positive numbers. We also relate the matrix coefficients to Kazhdan–Lusztig polynomials and to Bernstein functions. chi tea thoriumWeb1 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 … grapow hombruchWebCoefficient ring of Satake isomorphism. Let G be a split reductive group over local field F, G L be the (complex) Langlands dual group of G. Denote H to be the Z -Hecke algebra of G, that is the ring of G ( O F) -biinvariant Z -valued functions on G ( F). Let R ( G L) be the Grothendieck ring of finite dimensional representation of G L. grapow riverside ca