Irreducibility criterion for quasiregular representations of the group of finite upper triangular matrices (Q1400113)

The author defines an analogy of the quasiregular representation for the group of infinite-order finite upper triangular matrices. It uses \(G\)-quasi-invariant measures on some \(G\)-spaces. The author gives a criterion for the irreducibility and equivalence of the constructed representations which allows him to generalize Ismagilov's conjecture on the irreducibility of an analog of the regular representations of infinite dimensional groups.