Webone may consider two related rings: the spherical Hecke algebra attached to G(F), and the representation ring of the Langlands dual group G^. By the Satake isomorphism, these rings are actually isomorphic. However, the two realizations give rise naturally to two di erent bases and thus to two di erent sets of structure constants de ning this ring. Web30. nov 2004 · We also consider spherical Hecke algebras of the torus of SL 2 and construct the Satake isomorphism between two spherical Hecke algebras. In order to define the …
The spherical Hecke algebra for affine Kac-Moody groups I
WebThe spherical Hecke algebra for GL (2). Unramified principal series. The Iwahori-Hecke algebra. Statement of Casselman's new vectors theorem and uniqueness of Whittaker functionals. Lecture 4 (1 Nov): The Kirillov model; proof of new vectors theorem. Adeles and ideles. Strong approximation for SL (2). Modular curves as adelic double quotients. WebHowever, there is an alternative approach to developing an analytic theory of automorphic forms, based on the existence of a large commutative algebra of global differential operators acting on half-densities on the moduli stack of G -bundles. This approach (which implements some ideas of Joerg Teschner) is outlined here, as a preview of a ... town fridge las vegas
SOME EXAMPLES OF HECKE ALGEBRAS FOR TWO-DIMENSIONAL …
WebWe study the rational permutation braids, that is the elements of an Artin-Tits group of spherical type which can be written where x and y are prefixes of the Garside element of the braid monoid. We give a geometric characterization of these braids in type and and then show that in spherical types different from the simple elements of the dual braid monoid … WebWe will discuss Sakellaridis’s work on computing the eigenfunctions on spherical varieties under the action of the spherical Hecke algebra, which generalise the classical Casselman Shalika type formula. We will also discuss a variant of this formula, which involves the dual group of the spherical variety X and certain quotient of L-functions. town frisco