Elementary Representations of the Group B₀Z of Upper-Triangular Matrices Infinite in Both Directions. I - Kosyak, O.V. (Український математичний журнал, 2002)
We define so-called “elementary representations of the group B₀Z of finite upper-triangular matrices infinite in both directions by using quasi-invariant measures on certain homogeneous spaces and give a criterion for the irreducibility and equivalence of the representations constructed. We also give a criterion for the irreducibility of the tensor product of finitely many and infinitely many elementary representations.