Representations of McLain groups

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• 作者：Fernando Szechtman¹ ; ^{fernando.szechtman@gmail.com} ; Allen Herman ; ¹ ; ^{Allen.Herman@uregina.ca} ; Mohammad A. Izadi ^{izadi.mohammadali9@gmail.com}
• 关键词：20C15 ; 20C20
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：474
• 期：Complete
• 页码：288-328
• 全文大小：631 K
• 卷排序：474

文摘

Basic modules of McLain groups M=M(Λ,≤,R)M=M(Λ,≤,R) are defined and investigated. These are (possibly infinite dimensional) analogues of André's supercharacters of Un(q)Un(q). The ring R needs not be finite or commutative and the field underlying our representations is essentially arbitrary: we deal with all characteristics, prime or zero, on an equal basis. The set Λ, totally ordered by ≤, is allowed to be infinite. We show that distinct basic modules are disjoint, determine the dimension of the endomorphism algebra of a basic module, find when a basic module is irreducible, and exhibit a full decomposition of a basic module as direct sum of irreducible submodules, including their multiplicities. Several examples of this decomposition are presented, and a criterion for a basic module to be multiplicity-free is given. In general, not every irreducible module of a McLain group is a constituent of a basic module.