TY - JOUR

T1 - Groups Generated by Involutions of Diamond-Shaped Graphs, and Deformations of Young’s Orthogonal Form.

AU - Vershik, A.M.

AU - Tsilevich, N.V.

PY - 2020

Y1 - 2020

N2 - 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 of problems on such groups and their representations; and present results of some computer simulations. The case we are most interested in is that of the Young graph and subgroups generated by natural involutions of Young tableaux. In particular, the classical Young’s orthogonal form can be regarded as a deformation of our construction. We also state asymptotic problems for infinite groups.

AB - 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 of problems on such groups and their representations; and present results of some computer simulations. The case we are most interested in is that of the Young graph and subgroups generated by natural involutions of Young tableaux. In particular, the classical Young’s orthogonal form can be regarded as a deformation of our construction. We also state asymptotic problems for infinite groups.

M3 - Article

VL - 247

SP - 657

EP - 662

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -