31 citations · 105 across the 21 of their papers we have counts for
20 papers
Groups generated by involutions, numberings of posets, and central measures
Anatoly Vershik
We define a new class of countable groups, which are defined by its action on the set of monotonic numberings (diagrams) of an arbitrary finite or countable partial ordered set (po…
The problem of combinatorial encoding of a continuous dynamics and the notion of transfer of paths in graphs
Anatoly Vershik
We introduce the notion of combinatorial encoding of continuous dynamical systems and suggest the first examples, which are the most interesting and important, namely, the combinat…
On the decomposition of tensor representations of symmetric groups
P. P. Nikitin, N. V. Tsilevich, A. M. Vershik
Following the general idea of Schur--Weyl scheme and using two suitable symmetric groups (instead of one), we try to make more explicit the classical problem of decomposing tensor…
The theory of filtrations of subalgebras, standardness and independence
Anatoly Vershik
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of -algebras in measure spaces or decreasing sequences of subalgebras o…
On the relation of some combinatorial functions to representation theory
A. Vershik, N. Tsilevich
The paper is devoted to the study of some well-knonw combinatorial functions on the symmetric group $\sn$ --- the major index $\maj$, the descent number $\des$, and the inversion n…
Equivalence of the Brownian and energy representations
Sergio Albeverio, Bruce K. Driver, Maria Gordina +1
We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by quasi-invarian…