# Groups generated by involutions, numberings of posets, and central measures

@inproceedings{Vershik2021GroupsGB, title={Groups generated by involutions, numberings of posets, and central measures}, author={Anatoly M. Vershik}, year={2021} }

An infinite countable ordered set {P,≻,∅} with minimal element ∅ and no maximal elements is called a locally finite poset if all its principal ideals are finite. A monotone numbering of P (or of a part of P ) is an injective map φ : N → P from the set of positive integers to P satisfying the following conditions: if φ(n) ≻ φ(m), then n > m; φ(0) = ∅. The distributive lattice ΓP of all finite ideals of a locally finite poset {P,≻} forms an N-graded graph (the Hasse diagram of the lattice). A… Expand

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The Schur--Weyl graph and Thoma's theorem

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We define a graded graph, called the Schur–Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric… Expand

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