On the satake isomorphism
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: … 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.
On the satake isomorphism
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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 … 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 …
WebON THE SATAKE ISOMORPHISM G. LUSZTIG Department of Mathematics MIT Cambridge, MA 02139, USA Institute for Advanced Study Princeton, NJ 08450, USA … WebCoefficient 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.
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. 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 …
Web27 de mai. de 2024 · Download Citation ON THE SATAKE ISOMORPHISM In a 1983 paper, the author has established a (decategorified) Satake equivalence for affine Hecke …
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 … rbc online banking currency exchangerbc online banking guaranteeWeb2 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 … rbc online banking exchange ratesWebcompact 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. rbc online banking insurance quoteWeb29 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. sims 4 admiral\u0027s wreckage chestWebopen 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 … rbc online banking in canadaWebLet 𝑄 Q italic_Q be the set of all translations in 𝑊 W italic_W, that is the set of all 𝑡 𝑊 t\in W italic_t ∈ italic_W such that the 𝑊 W italic_W -conjugacy class of 𝑡 t italic_t is finite. It is known that 𝑄 … rbc online banking foreign exchange