Corpus ID: 236469090

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

  title={Groups generated by involutions, numberings of posets, and central measures},
  author={Anatoly M. Vershik},
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
1 Citations
The Schur--Weyl graph and Thoma's theorem
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 symmetricExpand


Three theorems on the uniqueness of the Plancherel measure from different viewpoints
We consider three uniqueness theorems: one from the theory of meromorphic functions, another one from asymptotic combinatorics, and the third one about representations of the infinite symmetricExpand
Groups Generated by Involutions of Diamond-Shaped Graphs, and Deformations of Young’s Orthogonal Form
With an arbitrary finite graph having a special form of 2-intervals (a diamond-shaped graph) we associate a subgroup of a symmetric group and a representation of this subgroup; state a series ofExpand
Ergodicity and totality of partitions associated with the RSK correspondence
We study asymptotic properties of sequences of partitions (σ-algebras) in spaces with Bernoulli measures associated with the Robinson–Schensted– Knuth correspondence.
Groups generated by involutions of diamondshaped graphs
  • and deformations of Young’s orthogonal form, J. Math. Sci. (N.Y.) 247, No. 5, 657–662
  • 2020