Groups generated by involutions, numberings of posets, and central measures
Abstract
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 (poset). These groups are generated by the set of involutions? and in the case of finite posets could be considered as generalization of Coxeter's symmetric groups. We discuss the problems concerned to infinite groups jf this type, in particular the problem of the descripton of invariant measures on the space of numberings (central measures)with respect to actions of those groups. The probelms are tightly connected with the new theory of representations of the generalizations of infinite symmetric group.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.13022
 Bibcode:
 2021arXiv210713022V
 Keywords:

 Mathematics  Combinatorics;
 20B07
 EPrint:
 3 pp, 3 Ref