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- W4303107276 abstract "A subspace representation of a poset $mathcal S={s_1,...,s_t}$ is given by a system $(V;V_1,...,V_t)$ consisting of a vector space $V$ and its subspaces $V_i$ such that $V_isubseteq V_j$ if $s_i prec s_j$. For each real-valued vector $chi=(chi_1,...,chi_t)$ with positive components, we define a unitary $chi$-representation of $mathcal S$ as a system $(U;U_1,...,U_t)$ that consists of a unitary space $U$ and its subspaces $U_i$ such that $U_isubseteq U_j$ if $s_iprec s_j$ and satisfies $chi_1 P_1+...+chi_t P_t= mathbb 1$, in which $P_i$ is the orthogonal projection onto $U_i$. We prove that $mathcal S$ has a finite number of unitarily nonequivalent indecomposable $chi$-representations for each weight $chi$ if and only if $mathcal S$ has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if $mathcal S$ contains any of Kleiner's critical posets." @default.
- W4303107276 created "2022-10-07" @default.
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- W4303107276 date "2011-03-05" @default.
- W4303107276 modified "2023-10-17" @default.
- W4303107276 title "Kleiner's theorem for unitary representations of posets" @default.
- W4303107276 doi "https://doi.org/10.48550/arxiv.1103.1085" @default.
- W4303107276 hasPublicationYear "2011" @default.
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