An inclusion of certain algebras of operators on Hilbert sapce is called a subfactor. It is a mathematical object with an extremely interesting representation theory that is similar in many ways to the representation theory of groups.
A subfactor is said to have infinite representation theory, or infinite depth, if its standard representation generates infinitely many non-equivalent irreducibles. Such subfactors are hard to come by, and only very few methods to explicitly construct examples are known. I will highlight one such procedure and discuss properties of these subfactors. The talk will be accessible to non-experts.