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On the Center of Generic hecke algebra

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Journal of Beijing Institute of Technology 2006年第1期15卷 119-122页

作者：魏丰鲍刚 School of Science Beijing Institute of Technolgy Beijing 100081 China

The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.

关键词： Coxeter group hecke algebra cellular basis center

REPRESENTATIONS OF AFFINE heckeALGE BRAS OF TYPE G_2

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Acta Mathematica Scientia 2009年第3期29卷 515-526页

作者：席南华 Institute of Mathematics Chinese Academy of SciencesBeijing 100190 China

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.

关键词： representation affine hecke algebra affine Weyl groups hecke algebra

Hochschild Homology of Tame hecke algebras

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Chinese Quarterly Journal of Mathematics 2014年第3期29卷 325-334页

作者： HOU Bo School of Mathematics and Information Science Henan University Kaifeng 475001 China

Let A be a tame hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.

关键词： Hochschild homology hecke algebra cyclic homology

Isolation of the cuspidal spectrum:The function field case

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Science China Mathematics 2022年第7期65卷 1331-1342页

作者： Li Cai Bin Xu Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China School of Mathematics Sichuan UniversityChengdu 610064China

Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula *** example,matrix coefficients of supercuspidal representations can be used as test functions for ***,they kill a large class of interesting cuspidal automorphic *** the case of number fields,multipliers of the Schwartz algebra are used in the recent work(see Beuzart-Plessis et al.(2021))to isolate all the cuspidal *** particular,they are suitable for the comparison of orbital *** multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups(see Beuzart-Plessis et al.(2021,2022)).In this article,we prove the similar result on isolating the cuspidal spectrum in Beuzart-Plessis et al.(2021)for the function field case.

关键词： cuspidal spectrum hecke algebra trace formula automorphic representation

HARMONIC ANALYSIS ON THE QUOTIENT k^x非汉字符号k\A^1非汉字符号A^1

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Acta Mathematica Scientia 2001年第1期21卷 21-28页

作者： Anton Deitmar School of Mathematical Sciences University of Exeter Laver Building, North Park Road Exeter, EX4 4QE Devon, UK

Let G be the semidirect product A1 ■ A of the adeles and the norm 1 ideles of a global field k. Let г be the discrete subgroup kx ■ k. In this paper the trace formula for this setting is established and used to give the complete decomposition of the G-representation on L2(г\G). It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.

关键词： Ideles adeles Selberg trace formula hecke algebra