On the satake isomorphism

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 … 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

[2005.13056] A note on Integral Satake isomorphisms - arXiv.org

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… Web10 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 … open the bay pod doors hal https://turnaround-strategies.com

[PDF] On matrix coefficients of the Satake isomorphism: …

Webopen 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 … 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. 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. ip. chicken

The Satake Isomorphism and the Langlands Dual - Zachary Gardner

Category:The Satake Isomorphism and the Langlands Dual - Zachary Gardner

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On the satake isomorphism

Spherical representations and the Satake isomorphism - Stanford …

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: … 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.

On the satake isomorphism

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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 · 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 ...

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

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openthebooks.com arizonaWebON 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 … open the books alaskaWebhere. What we will do is some calculations that suggest the general outline of the proof of Satake’s theorem. Suppose we have a decomposition K ($)K= ‘ i x iK. Since G(F) = … ipc-hfw5442t-as-ledWeb15 de jun. de 2011 · Quantum cohomology and the Satake isomorphism. We prove that the geometric Satake correspondence admits quantum corrections for minuscule … open the bay doors siriWebON 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 … ip chicken hawkWebSatake 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 open the book at pageWeb27 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 … open the book i\u0027m currently reading