2018
Том 70
№ 12

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

Kosyak O. V.

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 54 (2002), no. 2, pp 253–265.

Citation Example: Kosyak O. V. Elementary Representations of the Group $B_0^ℤ$ of Upper-Triangular Matrices Infinite in Both Directions. I // Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 205-216.

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