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4 votes
1 answer
304 views

Finite covolume of uniform lattice in quotient group

Let $G$ be a locally compact group, let $N \leq G$ be a (proper) closed normal subgroup and let $\Gamma \leq G$ be a uniform lattice, i.e., a discrete subgroup such that $G/\Gamma$ Is compact. Suppose ...
6 votes
1 answer
1k views

Classification of compact connected abelian groups

It is known that torsion-free compact abelian groups are exactly the product of the maximal solenoid group $\Sigma_{(2,3,\cdots)}$ (which is the Pontryagin dual of the additive group $\mathbb{Q}$ of ...
5 votes
0 answers
119 views

Characterizing Herz-Schur multipliers using coefficient functions of uniformly bounded representations

Let $G$ be a group and let $c > 1$ be a constant. We denote by $B_c(G)$ the space of all coefficients of the representations of $G$ which are uniformly bounded by $c$; more precisely, a function $f:...