On the satake isomorphism
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 … Web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
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 … 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. …
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 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:
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 … 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.
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 …
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. iphone 14 pro power adaptorWeb27 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 … iphone 14 pro pre order shippingWebconstruction 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). iphone 14 pro pre bookingWeb10 de dez. de 2013 · The Satake isomorphism allows us to analyze the structure of H (G;K) and hence understand spherical representations. To state the most general … iphone 14 pro picture tipsWeb2 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 iphone 14 pro price in californiaWebIn 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. … iphone 14 pro pretty casesWeb29 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. iphone 14 pro price in israel