TY - JOUR
AU - O. V. Kosyak
PY - 2002/02/25
Y2 - 2024/05/26
TI - Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 54
IS - 2
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/4056
AB - 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.
ER -