On the satake isomorphism
WebDERIVED SATAKE ISOMORPHISM AND IWAHORI-HECKE ALGEBRAS, [?, x3-4] 5 The reduction map A \K !A splits uniquely, and under our hypotheses induces an isomorphism on cohomology with coe cients in S H(A \K;S) ’H(A;S) Following Venkatesh, we make this identi cation for the remainder. To summarise, for the derived Hecke algebra of a torus … Web17 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.
On the satake isomorphism
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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 ... WebAbstract: 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.
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 … 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. …
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 … 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 …
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.
Web29 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. sharp and shiny knivesWebThe 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 ... porch table and chair sets cheapWebThe 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 … porch table and chairWeb2 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 sharp and tannan puneWebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … sharpand thier namesWebIn 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 … sharpandtypeWebisomorphism 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 ... porch table plans