On classification of σq-conjugacy classes of a loop group

JOURNAL OF ALGEBRA

卷:459

Article

Nie, Sian¹  Zhou, Peipei² 

[1] Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Sci & Technol Informat Assurance Lab, Sub Box 21,Box 7227, Beijing 100072, Peoples R China

关键词: Loop group;    sigma(q)-conjugacy class;   

DOI  :  10.1016/j.jalgebra.2016.03.026

来源: Elsevier

【 摘 要 】

Let k be an algebraically closed field and L = k((epsilon)) the field of Laurent series over k. Let G be a connected reductive group over k such that the characteristic of k does not divide the order of the Weyl group of G. For q is an element of k(x), the automorphism of L, defined by Sigma a(i)epsilon(i) bar right arrow Sigma a(i)(q epsilon)(i), induces an automorphism sigma(q) of the loop group G(L). We show that, when q is not a root of unity, the classification of sigma(q)-conjugacy classes of G(L) can be reduced to the classification of unipotent classes of (non-connected) reductive groups. As an application, we recover the classification (of sigma(q)-conjugacy classes) for G = GL(n). (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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