Crystal bases and simple modules for Hecke algebra of type D-n

doi:10.1016/S0021-8693(03)00350-8

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	Crystal bases and simple modules for Hecke algebra of type D-n
	Hu, J
	2003-09-01
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	267 期号:1 页码:7-20
摘要	Let H-C(B-n) (respectively H-C(D-n)) be the Hecke algebra of type B-n (respectively of type D-n) over the complex numbers field C. Let zeta be a primitive 2lth root of unity in C. For any Kleshchev bipartition (with respect to (zeta, 1, -1)) lambda = (lambda((1)), lambda((2))) of n, let (D) over tilde (lambda) be the corresponding irreducible H-C(B-n)-module. In the present paper we explicitly determine which (D) over tilde (lambda) split and which (D) over tilde (lambda) remains irreducible when restricts to RC (Dn) - This yields a complete classification of all the simple modules for Hecke algebra H-C(D-n). Our proof makes use of the crystal bases theory for the Fock representation of the quantum affine algebra U-q((sl) over cap (2l)) and deep result of Ariki's proof of LLT's conjecture [J. Math. Kyoto Univ. 36 (1996) 789-808]. (C) 2003 Elsevier Inc. All rights reserved.
DOI	10.1016/S0021-8693(03)00350-8
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000184522800002
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/18398
专题	中国科学院数学与系统科学研究院
通讯作者	Hu, J
作者单位	1.Beijing Inst Technol, Dept Math Appl, Beijing 100081, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Hu, J. Crystal bases and simple modules for Hecke algebra of type D-n[J]. JOURNAL OF ALGEBRA,2003,267(1):7-20.
APA	Hu, J.(2003).Crystal bases and simple modules for Hecke algebra of type D-n.JOURNAL OF ALGEBRA,267(1),7-20.
MLA	Hu, J."Crystal bases and simple modules for Hecke algebra of type D-n".JOURNAL OF ALGEBRA 267.1(2003):7-20.