The based ring of the lowest generalized two-sided cell of an extended affine Weyl group

doi:10.1016/j.jalgebra.2016.11.031

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	The based ring of the lowest generalized two-sided cell of an extended affine Weyl group
	Xie, Xun 1,2
	2017-05-01
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	477 页码:1-28
摘要	Let c(0) be the lowest generalized two-sided cell of an extended affine Weyl group W with unequal parameters. We first prove that certain conjectures of Lusztig (called Pl P15) hold for co, which implies the existence of the based ring of CO and then we determine the structure of the based ring. As an application, we use the structure of the based ring to study certain simple modules of the Hecke algebra with unequal parameters associated to W, namely those attached to co. Further we give a set of prime ideals p of the center Z of the affine Hecke algebra It such that the reduced algebra kpll is simple over K-p, where k(p) = Frac(Z/p) is the residue field of Z at p. In particular, we show that the algebra -1.10z Frac(Z) is split simple over the field Frac(2).
关键词	Affine Realm algebra Lowest two-sided cell Based ring P1-P15
DOI	10.1016/j.jalgebra.2016.11.031
语种	英语
资助项目	National Natural Science Foundation of China[11321101]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000396380500001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25167
专题	中国科学院数学与系统科学研究院
通讯作者	Xie, Xun
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Xie, Xun. The based ring of the lowest generalized two-sided cell of an extended affine Weyl group[J]. JOURNAL OF ALGEBRA,2017,477:1-28.
APA	Xie, Xun.(2017).The based ring of the lowest generalized two-sided cell of an extended affine Weyl group.JOURNAL OF ALGEBRA,477,1-28.
MLA	Xie, Xun."The based ring of the lowest generalized two-sided cell of an extended affine Weyl group".JOURNAL OF ALGEBRA 477(2017):1-28.