A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem already appears in the analysis of the set of all solutions to the three chain completion problem. The interpolants are upper triangular operator matrices of which the columns induce contractive operators. The set of all s...

We consider certain conditions for abstract lattices of commuting squares, that we prove are necessary and sufficient for them to arise as lattices of higher relative commutants of hyperfinite II1 inclusions of finite Jones index. In particular, we construct a one parameter family of inclusions of hyperfinite II1 factors N ⊂ M, with trivial relative commutant (Nλ)′∩Mλ = C with the Jones index [...

We study topological defect lines in two character rational conformal field theories. Among them one set of theories are commutant pairs $E_{8,1}$ theory. Using these we construct partition function the $E_8$ find that defects preserve only a part current algebra symmetry. also determine $c=24$ CFTs using 2 and that, with appropriate choice pairs, all symmetries c = 24 CFTs.