SL2 representations and relative property (T)

被引：0

作者：

Zhang, Zezhou ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, MOE, Beijing 100875, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2024年 / 639卷

关键词：

Relative property (T); Admissible lattices; Kac-Moody group; Expander graphs; Spectral gap; sl2; CHEVALLEY-GROUPS; WEYL MODULES; SPECTRAL GAP; II1; FACTORS; KAZHDAN; SUBGROUPS; PRODUCTS;

D O I：

10.1016/j.jalgebra.2023.10.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate relative property (T) of Kazhdan-Margulis for (SL2(R) alpha Rn, Rn), mainly where R is a discrete finitely generated commutative ring. The action of SL2(R) on Rn is defined through admissible lattices of the irreducible representations of sl2(C). Both positive and negative results are obtained. Applications of these results will be given, including the establishment of property (T) for certain KacMoody type groups over commutative rings. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：281 / 326

页数：46

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