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… WebThe 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 …
GEOMETRIC SATAKE, SPRINGER CORRESPONDENCE, AND SMALL …
Web24 de set. de 2008 · of the Satake isomorphism for this algebra, relating it to integrable repre-sentations of the Langlands dual a ne Kac-Moody group. In the next publication we shall use these results to de ne and study the notion of Hecke eigenfunction for the group G a . 1. Introduction 1.1. Langlands duality and the Satake isomorphism. Let F be a global … 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 … northland school division website
ON SATAKE PARAMETERS FOR REPRESENTATIONS WITH …
Web1 de dez. de 2024 · Abstract: In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper we give new proofs for … 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: Webconstruction 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). how to say story in french