On the satake isomorphism
Webhere. 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) = … 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 …
On the satake isomorphism
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WebON 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 … 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 ...
Webcompact 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. 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…
WebTraductions en contexte de "anneau du groupe" en français-anglais avec Reverso Context : des moyens permettant d'exciter séparément sur chaque anneau du groupe, des mémoires WebBegins 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 …
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 …
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 … precautions to avoid snake biteWebLet 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 … scooters lawn care flWeb27 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 … scooters lawn careWeb27 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 … scooters largo flWeb2 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 precautions to yellow fever vaccineWeb27 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 … precautions to be taken in diwaliWeb23 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: … scooters lawn care springfield illinois