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• W2022066140 abstract "In the paper we completely describe characters (central positive-definite functions) of simple locally finite groups that can be represented as inductive limits of (products of) symmetric groups under block diagonal embeddings. Each such group $G$ defines an infinite graph (Bratteli diagram) that encodes the embedding scheme. The group $G$ acts on the space $X$ of infinite paths of the associated Bratteli diagram by changing initial edges of paths. Assuming the finiteness of the set of ergodic measures for the system $(X,G)$, we establish that each indecomposable character $chi :G rightarrow mathbb C$ is uniquely defined by the formula $chi(g) = mu_1(Fix(g))^{alpha_1}...mu_k(Fix(g))^{alpha_k}$, where $mu_1,...,mu_k$ are $G$-ergodic measures, $Fix(g) = {xin X: gx = x}$, and $alpha_1,...,alpha_kin {0,1,...,infty}$. We illustrate our results on the group of rational permutations of the unit interval." @default.
• W2022066140 created "2016-06-24" @default.
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• W2022066140 date "2011-05-31" @default.
• W2022066140 modified "2023-09-27" @default.
• W2022066140 title "On Characters of Inductive Limits of Symmetric Groups" @default.
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