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Spherical hecke algebra

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 https://askerova-bc.com

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

The Geometric Satake Equivalence - University of California, …

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Spherical hecke algebra

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Web29. jan 2012 · Stéphane Gaussent (IECN), Guy Rousseau (IECN) We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean … WebI will talk about Integrable modules of loop-toroidal Lie algebras with finite dimensional weight spaces, when a part of the center acts non-trivially on the modules. ... Through the study of the Hecke operator, we will explore congruences of various obejcts, including the Fourier coefficients of modular functions and mock modular functions ...

Spherical hecke algebra

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Webthe pro-p-Iwahori Hecke algebra for any (G;R). It is a fundamental tool for the theory of the representations of Gover a eld Cof characteristic p: the inverse Satake isomorphism for spherical Hecke algebras, the classi cation of the supersingular simple modules of the pro-p-Iwahori Hecke 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-

WebIt states that the spherical Hecke algebra of a p-adic reductive group can be identified with the Grothendieck ring of the category of representations of the dual group. In this setup, one may study the Whittaker module, which contains information about unramified Whittaker functions and show that it is isomorphic to the spherical Hecke algebra. Web10. dec 2013 · The Hecke algebra H (G;K) is called the spherical Hecke algebra with respect to K. Note that this notion depends on the conjugacy class of K. By de nition, every vector in a smooth representation is xed by some su ciently small compact open subgroup. Spherical representations with respect to Kmay thus be thought of, in some sense, as the ...

http://www.math.ac.cn/xshd/sxsjz/202402/W020240312493255635326.pdf WebIn mathematics, a Hecke algebra is classically the algebra of Hecke operators studied by Erich Hecke. It may also refer to one of several algebras (some of which are related to the …

WebLi TANG Haiting CHEN Shoufeng SHEN Yongyang JIN. Abstract In this paper, the authors obtain the Dunkl analogy of classical Lp Hardy inequality for p>N+2γ with sharp constant ,where 2γ is the degree of weight function associated with Dunkl operators, and Lp Hardy inequalities with distant function in some G-invariant domains.Moreover they prove two …

WebThe Iwahori Hecke algebra is closely related to the Temperly-Lieb algebras which arise in both statistical physics and quantum physics. The related ex-amples were key in the discovery of quantum groups. Iwahori Hecke algebras were used in Vaughn Jones’ rst … ny state reserveamericaWebThe rational Cherednik algebra 5 3.2. The spherical subalgebra 7 4. Representation theory at t 6= 0 8 4.1. Category O 8 4.2. Dunkl operators and KZ functor 10 4.3. Primitive ideals and supports 11 ... The nite Hecke algebra appears as a coset algebra for a group of the same type as G, over a nite eld. ny state resultsWeb11. apr 2024 · It introduces the Hecke algebra of $G=GL_n(F)$ for a non-Archimedean local field F as the space of compactly supported, bi-$K$-invariant functions on $G$, … magic wine tour wolfvilleWebIchiro Satake[1963]studied such algebras to define the spherical functions and proved, in particular, that HK is commutative for a good choice K s of K, maximal compact. The corresponding convolution algebra HK s D s.G/is now called the spherical Hecke algebra. From[Iwahori and Matsumoto 1965], we know that there exists an interesting open ... magic wings butterfly museum deerfield maWebAt the same time the algebra K[Λ] may be viewed as the ring of algebraic functions on the dual maximal torus T′ in the dual group G′. Together, these isomorphisms allow the identifi-cation of characters of the spherical Hecke algebra with semisimple conjugacy classes in G′. On the one hand, the Hecke character corresponds to a certain magic wings keyboard cgnage brithnessWebIn mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) … magic wings gamer keyboard softwareWebSoliton theory Solitons are special solutions to nonlinear partial differential equations but they also parametrize surfaces such as the one depicted above magic wings butterfly conservatory coupons