ИСТИНА

Consider a triple product G of infinite symmetric groups, the diagonal $K$, and subgroups $K(n)$ in $K$ fixing first $n$ points. We describe double cosets $K(n) \ G/K(m)$ in terms of two-dimensional surfaces with special colored triangulations. We show that they form a category (multiplication is similar to concatenation of cobordisms) and unitary representations of $G$ produce representations of this category.