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• W2020126760 abstract "A subspace representation of a poset S={s1,…,st} is given by a system (V;V1,…,Vt) consisting of a vector space V and its subspaces Vi such that Vi⊆Vj if si≺sj. For each real-valued vector χ=(χ1,…,χt) with positive components, we define a unitary χ-representation of S as a system (U;U1,…,Ut) that consists of a unitary space U and its subspaces Ui such that Ui⊆Uj if si≺sj and satisfies χ1P1+⋯+χtPt=1, in which Pi is the orthogonal projection onto Ui. We prove that S has a finite number of unitarily nonequivalent indecomposable χ-representations for each weight χ if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner’s critical posets." @default.
• W2020126760 created "2016-06-24" @default.
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• W2020126760 creator A5067513301 @default.
• W2020126760 date "2012-07-01" @default.
• W2020126760 modified "2023-10-16" @default.
• W2020126760 title "Kleiner’s theorem for unitary representations of posets" @default.
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• W2020126760 doi "https://doi.org/10.1016/j.laa.2012.02.030" @default.
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