@article{Kosyak_2002, title={Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I}, volume={54}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/4056}, abstractNote={We define so-called “elementary representations” $T_p^{R,µ},\; p ∈ ℤ$, of the group $B_0^ℤ$ 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.}, number={2}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Kosyak, O. V.}, year={2002}, month={Feb.}, pages={205-216} }