Description of groups generated by involutions of two-row Young tableaux

Anatoly Vershik proposed a program for the systematic study of a class of groups generalizing the class of classical Coxeter groups, namely groups generated by natural involutions of standard Young tableaux and, more generally, by involutions of path spaces of some graphs. The author, solving the questions posed by Vershik, continues to study a series of groups for more complex Young diagrams. In this paper, significant results are obtained about the group corresponding to an arbitrary two-row diagram.