WebLet H be an (extended) affine Hecke algebra. It contains the Hecke algebra H f of the finite Weyl group W f as a subalgebra. The set of elements of H which are “invariant” under left and right multiplication by H f is called the spherical Hecke algebra Hsph. The Satake isomorphism identifies Hsph with Z[v±1][X∨]W f where X∨ is the ... WebTitle: Latticed based Cryptography and its Applications. Abstract: Since the first use of lattices in the Knapsack cipher system in 1982 for cryptographic purposes, lattice-based cryptography has begun to draw attention to its potential cryptographic applications. Above all, with the fact that lattice-based problems are resistant to attacks by ...
Representations of affine Kac-Moody groups over local and global …
Web16. apr 2024 · Overview. Our goal today is to finish the proof of the main identity for all functions in the spherical Hecke algebra of .For any (unramified everywhere) cuspidal automorphic representation of , the LHS via the analytic spectral decomposition and the RHS via the cohomological spectral decomposition (discussed below) would imply the identity … WebOne may study the spherical Hecke algebra Hof G(O)-biinvariant compactly supported C-valued measures on G(K). The Satake isomorphism is a canonical isomorphism between … ny state resident meaning
The Geometric Satake Equivalence - University of California, …
WebA tutorial introduction gives the requisite background material. The techniques used to prove the main results run the gamut of modern harmonic analysis such as representation theory, spherical functions, Hecke--Bochner formulas and special functions. Graduate students and researchers in harmonic analysis will greatly benefit from this book. 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 ... 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 magic wine glass