3 citations · 7 across the 12 of their papers we have counts for
11 papers
-dependence of matrices
Natalia Tsilevich, Yahel Manor
We introduce the notion of -dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which g…
Asymptotics of higher Lie characters
Ron M. Adin, Yuval Roichman, Natalia Tsilevich
Higher Lie characters form a distinguished family of symmetric group characters, which appear in many areas of algebra and combinatorics. An old open problem of Thrall is to decomp…
The Schur--Weyl graph and Thoma's theorem
A. Vershik, N. Tsilevich
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…
Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form
A. Vershik, N Tslevich
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; sta…
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…
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…