Web9. jún 2024 · Hecke algebra is a term for a class of algebras. They often appear as convolution algebras or as double coset spaces . For p-adic algebraic groups Hecke … WebarXiv:math/0303190v1 [math.RT] 16 Mar 2003 DOUBLE AFFINE HECKE ALGEBRAS AND CALOGERO-MOSER SPACES ALEXEI OBLOMKOV Abstract. In this paper we prove that the spherical subalgebra eH1,τe of the double affine Hecke algebra H1,τ is an integral Cohen-Macaulay al- gebra isomorphic to the center Z of H1,τ, and H1,τeis aCohen-Macaulay …
Representations of affine Kac-Moody groups over local and global …
WebWe will introduce various Hecke algebras attached to G, in particular the spherical Hecke algebra and the Iwahori-spherical Hecke algebra. We will study the representations of these algebras, and will explicit their relation with the above mentioned decomposition. 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. cloudformation lambda api gateway
1. The elliptic Hall algebra, the spherical DAHA and the polynomial ...
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. WebHecke algebra. Hopf algebra. Coideal. Let W be a Coxeter group. The goal of the paper is to construct new Hopf algebras that contain Hecke algebras H q(W)as (left) coideal subalgebras. Our Hecke-Hopf algebras1 H(W)have a number of applications. In particular they provide new solutions of quantum Yang-Baxter equation and WebHecke algebra analogue of the proof given by Kato [Ka] for a ne Hecke algebras. Proofs of this criterion for graded Hecke algebras have appeared in [Ch1, Kr2] but ... ered but the representations classi ed were spherical and tempered. An important consequence of our rank two construction is that it establishes a \Springer corre- cloudformation lambda inline