Complex sentence: They are rather mysterious: they do not turn up very often, and seem to exist by accident, and were sometimes overlooked in some earlier claims to have classified the irreducible unitary representations of certain groups.
Split into simpler sentences: They are rather mysterious: they do not turn up very often, and seem to exist by accident. They were sometimes overlooked, in fact, in some earlier claims to have classified the irreducible unitary representations of certain groups.