Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I

• Date: 2002
• Main Authors: Kosyak, O. V., Косяк, О. В.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4056
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 representatio...